It doesn't ring any bells, it mostly reminds me of "Abu Hanifa", who founded one of the four main Sunni schools of law, but that wouldn't make much sense in this context. Though it could still be the name she's thinking of, I guess, it's just calling it a really particularly moderate sect is a bit odd when it's the largest of the four mainstream schools in Sunni Islam.

If he converted before marrying her, none of the major Islamic denominations would oppose it, in theory - of course real life is not always the same as theory, and in practice some families certainly would have issues with that.