In fact, "lines" is superfluous and, in fact, a bad choice, since wireless connections are just as convenient and effective. Since this is a technical (not literary) translation, we need an expression that reflects the meaning, and is actually used in Portuguese:

A close translation of the last phrase (from "plus the time") would go:

...além da economia de tempo e custos conseguida ao compartilhar arquivos (digitais) via conexão de rede (de dados), em contraste com despesas de telefonema ou de serviço de mensageiro.

However, since the original is not that well written (as an example, the network feature relevant to this context is not sharing but transmitting), one would do better with:

...além de economizar tempo e dinheiro, ao transmitir diretamente (seus) faxes (digitalmente) através de redes (de computadores), evitando assim despesas de telefonema ou de serviço de mensageiro.

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Note added at 4 hrs (2010-04-17 16:45:36 GMT)
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Somehow the italic tags didn't work for sharing, and transmitting ;-)