"is fitted to become" also sounds strange to me, but it must be correct, since it gets over 16000 hits on Google, where it is used in professional websites.

--responding to @needs native check--
I would have said "is suited to become" which gets marginally more google hits ;) or "is fit to become" (at 87,000 hits.)

re: @needs native check
Ouch, I dislike this Google method. "is fitted to become" might well come up in the context of building and property, eg: "this room is fitted to become a kitchen". "is suited to become" or "is fit to become" sound correct to this native.

Here's a quote from Edith Wharton: "The Age of Innocence" What does it matter if she had spent her girlhood in seclusion, provided she is free to emerge from it at the moment when she is fitted to become a real factor in social life?" The source of the Tatoeba sentence seems to be from this dictionary:http://dict.longdo.com/index.ph...&search=fitted

I would tag it as archaic.

I wouldn't actually tag it as archaic. That example you provide, Dejo, does seem fine, because it follows "when". I believe the when clause means the tense works. Also, it says that example comes from the Tanaka Corpus, which would make sense.