Partially solved it myself.
Seems highly nonsensical, but this is what i have to do to make it work:
(-Both computers share the same TV-monitor)
-Computer A is turne on
-Switch input on the tv to Computer B
-Turn on Computer B
-Wait for log in screen to appear
-Switch TV-input to Comupter A
-Activate share screen
-Log in as adminstrator
No idea why the tv input settings affects share screen, but it does.