Well WoodLane, as most of the other comments have said, congrats to you, as you've made all the right moves, and have gained yourself a lucky new cat!
You've also had a bit of luck, as new arrivals can provoke some hissy fits, even a spat or two, but you seem to have avoided that. Our present cat seems to hate all others, though we heard he lived with three, perhaps that caused it?!
And for QuaintIrene, yes, that can happen, cats do indeed vote with their feet! We gained one some years ago, she'd got fed up being used as a toy by 2 little children, so came and found us. Our existing cat at the time soon got over the insult, as she (a Mastermind of cats), was able to lord it over a docile and much dimmer companion, who in turn was happy to have a quiet household. We made sure we fed the bossy one first (about 30 seconds difference), seemed to keep everyone happy.
Oh, PS, ignore any suggestion about re-contacting the woman who thought it might be hers. If she'd had a problem, she could have phoned.