The amount of current we can get through the wire without superconductivity breaking down is proportional to the cross-section of the wire.
Multiply that cross-section by the several thousand lightyears to the closest magnetar and you have a LOT of wire.
That means you need a lot of energy to position it. Simply dropping it off from a moving rocket isn't good enough, the wire needs to be stationary.
In fact, it's probably more energy than you could ever hope to transfer even in millions of years of operation.
Once you have the wire in place, you still need to worry about things like galactic drift, objects passing through the space occupied by the wire etc. so it's unlikely you could actually keep the wire in place for millions of years without needing to re-string it.
Oh, and the dynamo might not work as well as you want it to because superconductivity also breaks down in intense magnetic fields.