Mapping local shares to Share Point online

Hi all. What sounds like i should be simple is turning out to be not.

In a domain environment, we naturally have lots of file shares. We want these shares to live on Share Point now, not on local servers.

I can copy the data using Share Point Migration Tool, that bit is fine, we can also create Share Point sites for each share, set permissions on those sites no problem.

How do we get it so that when a user logs into a domain PC, they automatically get those Share Point document libraries mapped in This PC?