Stray cat strut

Here in Phoenix there is a big stray cat problem. Pretty much anywhere you go you'll see a stray kitty or two just roaming around...it's pretty sad. We live in an apartment and there are about five cats we see walking around that we're not sure if they're strays or just outside cats on the prowl. One kitty in particular seemed to live in the bushes in front of our apartment. I call her a 'she' but really I have no clue if it's a
boy or girl because she won't let us touch her and I've always felt it was kind of rude to look at a cat like that.

We started leaving food outside for this kitty which I started calling Black Cat because guess what-she's black! There's also Skinny Black Cat, Grey Kitty and Fat Striped Cat walking around out there. Anyway, black cat would
wait for us to totally leave the food alone
before coming to eat. If we even opened the door to go outside while
she was there she'd take off like a rocket. Eventually she would kind of hang around as we were leaving the food out, like sit there at a distance but still not getting anywhere near us.

When it started getting cold I made her a bed on our porch. Just a box with some old blankets but I felt really bad that she was out in the cold all the time. She started sleeping in it right away, so I guess she liked it! After that she got a little more friendly and would not orally take off if we came outside to feed her. She still wasn't approaching us but at least she wasn't completely heading for the hills the second we made a move around her.

Last week I guess she got brave because I found her walking around our living room! Oh yeah I don't think I've mentioned that we do actually have a cat of our own, an orange Tabby called Jax. Jax & Black Cat are total BFFs. So maybe he's been telling her we're a nice family and she should join us. We have a kitty door so Jax can come & go as he pleases and this is how Black Cat came in. The first few times she would of course make a mad dash for the exit as soon as she spotted us. Now it's been about a week and she'll come in, eat, sleep in the new bed I gave her (an old doggie bed but it's really cushy) as long as we don't try to pet her. It's been months of feeding her, she sleeps either on our porch or in our living room but she's still too scared to let us pet her.

I wonder how long it will take before she lets us snuggle her? Will it ever happen?