It used to be easy to find the latest Patchfinder.exe, which allows you to see which versions and patches are installed on a machine. For the life of me, I can't locate that program anymore in the downloads area. I've also checked in the patches download area, but nothing like that is there.
Did the name change or did Esri stop making it?
I have copy of the 10.6.1 version if there were a way to get it to you.
I really appreciate the offer, but as a matter of policy we can only acquire software from vendor's directly. I'll contact Esri support since I haven't seen any ideas of where to find them now. If I get a helpful answer I'll share it here.