If $ is first character of password then the GUI change app will not confirm at all. Get invalid password message.
If $ is the last character of PW then it is confirmed and will work normally for login.
If $ appears anywhere else in the PW then the PW is confirmed as valid but does NOT work for login.
Similar issue with "
I do not believe this is a keyboard setting issue.......
Using command line setting sudo passwd pi or passwd pi works fine with $ or " anywhere in the password.
See forum posts:
https://www.raspberrypi.org/forums/viewtopic.php?f=66&t=209384#p1294107
https://www.raspberrypi.org/forums/viewtopic.php?f=66&t=217795