This isn’t that complicated. Under no circumstances do you discuss financial information or provide access to your computer to someone who has called you. If it’s urgent call them back on a number you can verify.
You know, as I read this and see someone allowing a stranger take over their computer, I really just sort of mentally move on, sort of like passing a road kill on the highway. Sorry it happened, but nothing I can do about it. Some people simply deserve to get scammed, I’m not going to worry about them. You can’t teach IQ.