To anyome having issues with the black screen pop up when signing in with Facebook.
I will share how I did it to see if anyone else who has already tried to do it and it didn't work.
1- In my game I had another character (not linked to Facebook), what I did was delete that character, I got the option to restart and then I accepted.
2- I re-entered the game to verify that that character was not there, that it is completely empty.
3- I closed my Facebook session in the browser, I already had the Facebook apk uninstalled.
4- I restarted my cell phone and then installed the game v5.2.2
5- When I opened the game, I actually didn't get any "update the game" announcement, so I let the character creation menu download.
6- After that, I was finally able to do the linking process with Facebook, I linked and gave it the option to upload my character data.
7- When downloading the data of my main pj, the "update" ad appeared, but I simply ignored it and let it download the others.
8- After a while, I updated to v5.3.0 to verify that everything was going well, I opened the game again and it started with my main pj, then seeing everything solved, I ended up updating to v5.3.1
Note: Start saving 3 versions of the game on your devices in case it happens again in the future and do not despair by searching Google for other versions where they do not have the same "signature", save 2 previous versions and the current one. At least I'll start doing it like this and be cautious. I hope it helps you, good luck.