Same LogMeInRescue remote remote session split between two separate computers

In a recent windows 10 support session with microsoft I was unable to access any microsoft site.  We established a remote session with my xp  computer first.  The tech sent me a "link" to something that allowed me to download "Support-LogmeinRescue.exe to an external usb drive on that computer.  I think I remember a warning that it would not work with that version of windows.  May have gotten anoither 6 digit code as well.  The result was that I was able to move the external HD to the faulty Windows 10 computer,  run it from there and establish a remote session with windows 10.  The odd thing is the box for the xp session remained active and never appeared on the win 10 machine.  When I attempted to stop the original session on the xp machine it disconnected the session on the win 10 machine.  I need to repeat this so that a level 2 tech can access my windows 10 machine.   I did not think to screenshot the xp machin so I do not know what the link was.   Do you have any idea what occurred and how to repeat it?  I am desperate }:

My only guess is that there is a key in the exe file that I downloaded that linked it to the first xp session.  When I tried it with another tech (and a new session on the xp machine) running the first copy of Support-LogMeInRescue.exe would not connect. 

I know it sounds bazaar,  but it really happened.