From my understanding these need to be sent to -centro adjudicado- for approval and then the centre will send them to continue the process.

“Informar favorablemente o desfavorablemente”, Spanish legalese. This is my explanation of its meaning, both in a general scenario, but also applicable to this particular case.
Both previous answers are wrong because the “approval” does not depend on the intermediate organ (= comisión de docencia del centro adjudicado), which “merely” issues a report, in this case endorsing (= favorablemente) a final approval of the applications (= solicitudes). But the final decision of approval (or refusal) does NOT depend, and this is the key point here, on this intermediate organ, but on the final decision body, in this case a single person, the “titular de la Dirección General de Ordenación Profesional del Ministerio de Sanidad”, who will make the final decision, i.e. either in favour or against the approval (= resolución que proceda).
So I have to strongly disagree with the previous suggestions, but also with the translation “to process the request”, because “informar favorablemente” is certainly more than a mere processing of the request, it is a “favourable report” requesting the acceptance of the applications by this final decision “body” (here a single person).
Which means that in this intermediate stage NOTHING is decided, it is just an intermediate stage prior to the final decision.


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Note added at 23 hrs (2024-04-25 12:07:41 GMT)
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This is a different context, but the meaning of “informar favorablemente” is identical. As we can see in this particular case, the “Fiscal General del Estado”, i.e. the Spanish Prosecutor General or head of the Public Prosecutor's Office, merely makes a proposal or suggestion (= hará la propuesta en tal sentido), but he does not decide anything.

https://www.fiscal.es/documents/20142/0fb9b589-828b-e0f7-5b9...
El Consejo Fiscal informa sobre la provisión de destinos vacantes convocado por orden JUS/1137/2012 en el sentido siguiente:
I.-El Consejo Fiscal acuerda por unanimidad informar favorablemente la propuesta de renovación de XXX XXX XXX como Fiscal de Sala del Tribunal Supremo. El Fiscal General del Estado hará la propuesta en tal sentido.


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Note added at 1 day 21 hrs (2024-04-26 09:42:21 GMT)
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@Catherine. To further clarify things:
The “recognition of prior learning” process encompasses several stages. It is no surprising that you are puzzled since this process is complex even for Spaniards themselves (after all we are dealing here with the intricacies of the Spanish administration, a labyrinth in itself!).
Stages of the recognition process (abridged):
1) Once the application is submitted by the interest party (= medical student), it is analyzed by the first “body” (better than “organ”), which is the “comisión de docencia del centro adjudicado”.
2) This body, the “comisión”, issues a favorable report (NO approval at this stage, the key point!, they do not have the capacity to approve or reject the submitted applications). They just issue a report to allow the continuation of the process in case of a favourable assessment. If the report were unfavourable, the process would come to an end at this early stage! Hence, a favourable report is the prerequisite for the process to be continued.
3) The application is then submitted to the “Registro Nacional de Especialistas en Formación” (cannot say much about what they do, no context available!).
4) After examination (= consulta) through the “comisión nacional de la especialidad de la plaza adjudicada”, the application is then forwarded to the final body, yes, the “decision-making body”, which is the head (= persona titular) of the “Dirección General de Ordenación Profesional del Ministerio de Sanidad”. This person has the final say in the matter and can approve (yes, finally, the approval) or reject the request for recognition.

Well, this is it :-). I hope to have contributed by means of this additional explanation to a better understanding of the whole process.


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Note added at 13 days (2024-05-08 08:35:05 GMT) Post-grading
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To whom it may concern/to my dear colleagues of ProZ.com,

What has happened in this KudoZ is the greatest disappointment I have ever experienced at KudoZ/ProZ. Truly, I have lived some others before, but none comparable to this one. A fully wrong answer, which received 5 agreements, before my own (fully right) answer was posted, was chosen “as most helpful” by the “peer agreement” system. I knew this was the likely outcome if the
asker did not close the question fairly, which she did not do in the end.
It becomes obvious that I should have posted a disagree from the very beginning, which is what the answer chosen as most helpful really deserves, but instead I just posted the “politically correct neutral” comment, which is fully useless, as we can see here in this case (the recipient just remained silent, and we all know: “Silence implies consent”).
Yes, yes, I know that ProZ reminds us all, i.e. KudoZ participants, “not to take it personally” if the right question is disregarded (and a wrong answer is chosen as most helpful instead). Yes, I know, this happens on a daily basis, true, but what has happened here goes beyond what I deem the acceptable limit of my tolerance.
All my effort to explain a very difficult context was disregarded, ignored, despite the asker´s comment “ok thank you. That does actually make more sense”. Obviously, I shall not comment anything else on what I feel regarding the asker´s approach to this query. The reason for my reservation is evident.
To my friends at the ProZ.com staff: The peer agreement system you created some years ago is a failure in itself. It simply does not work and is doing a terrible damage to a site I have very much loved and respected. And because I respected it, I need to send this warning to you: Do apply the necessary changes to reconsider the “peer agreement” method for closing questions now when there is still time to do it. It is preferable to have a question open for years or “ad infinitum” to force its closing by means of the “peer agreement” system and achieve a result like this one. This one may be an extreme example of unfairness, true, but it is necessary to bear it in mind. If you properly analyze what has happened here, you do not need to know why I am saying this.
I shall never ever take part again in any queries posted by this asker. I am considering now if I should stop participating in KudoZ at all.


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Note added at 13 days (2024-05-08 08:39:02 GMT) Post-grading
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A correction:
Yes, yes, I know that ProZ reminds us all, i.e. KudoZ participants, “not to take it personally” if the right ANSWER is disregarded (...)