As others have written, I also see the Federation as a melting pot of ethnicities and cultures. I don't think there's any issue with your Amarr character either being born in the Federation, or finding a reason to become a citizen.
I might approach it from the defining characteristic of the Amarr, that of religion. If your character has a religious background, perhaps they went to the Federation as a missionary (from what I read, there's a lot of believers there since freedom of religion is a facet of their embrace of difference) and perhaps once there, the more liberal practice appealed? I note a lot of Amarr RPers tend towards the liberal wing, being uncomfortable with slavery, for example. Perhaps your character took this to a new, more tolerant society?
One story I was fascinated by was the Kador invasion of Solitude some years ago (which was recently explained by a love story). Maybe your character was part of this failed invasion, and taken as a prisoner of war. There's plenty of evidence of PoWs deciding to stay in their captor's homeland (lots of German PoWs from WW2, for example, chose to settle in Britain rather than go home). Maybe, like Uriam Kador, your character fell in love with a Gallente? This might also explain your absence, having been in a camp for the while, and give all sorts of starting points for RP with both Amarr and Federation players.
Just some thoughts provoked by all the lore I'm reading! Hope it might be of use or at least, help develop a thought or two.