Migration Assistant from drives removed from my MBP

My old 2011 17" MBP finally bit the dust, another case of failed video card so a certified apple service removed my two drives. One drive is the original and has the system and all applications on it.

I am going to contact him tomorrow, however I wanted to ask this community.

When I started to execute the Migration Assistant, first the only option applicable was to select from a MAC. I only have the drives which the appropriate one was connected to my new MBP via. USB. After I did that, the Migration Assistant was searching for some time so I cancelled it.

The service consultant said that I could use the Migration Assistant but he was closing Saturday or he would have migrated it for me.

Any suggestions?

Thank you