Restoring process blocked by Administrator password

So I bought a bright and and shining Mini Mac 512, and I try to restore data from my old iMac 2010, macOS 10.13.

Both computers have the Migration Assistent activated. So, on the Mini, I give it a 'go'.

But then, several steps later, I am told that on the iMac an Administrator is active. I have to give his password. But I have no idea… I tried everything, but to no avail.

I have searched how to reset the password or how to remove the Administrator. Nothing worked…

In the Preferences panel, I do not see a user Administrator. I called Apple Support, they could not help me either. The suggested I'd use my Time Machine backup. But that's another problem, the Mini does not even see the TM.

So I am pretty frustrated. Who can help me in killing this Administrator?

Thanks a lot.