Why do you "need" an abbreviation? Once again, it needs to be repeated here that just because the German text has an abbreviation it does not mean that the English text can or should have an equivalent abbreviation.
IF "finac" is used in a native English-speaking/English-based environment (and not as a pseudo-English term in a German-based/German-speaking environment), it would be an in-house term, and I strongly suspect most others would have no idea what it means. The same holds with "FA."
Regarding the links in #6 "proving" that FAS is used: A look at the quality of the English in the mitsoftware.com site and its source country (Malaysia) shows that that site is not an authoritative source. The U of C site is referring to that university's specific accounting system and not a general term for Financial Accounting.
The reference in #4 also shows that FAS is the name of a specific system at that university and the abbreviation is not used until after "Financial Accounting System" has been used. And, if you look at
http://f2.washington.edu/fm/toolkit/budget-ma... as well as other Financial Managment sites for the university, "financial accounting" is the term they use when not referring to a specific software system.
#5 is right: If FA is used in the English-speaking world, it is nowhere near as widespread as "FiBu" is in Germany. (And it's no surprise that "FIBU" comes through in Linguee -- there are tons of poor translations on there!
Summary: Don't invent English abbreviations just because they are common in German(and a handful of google hit is proof of nothing)!
