When I sold my old rifle, I pulled the scope and left it in the rings. When I put the scope on my new rifle, can I just re-mount it in the rings as is? ...or should it be removed from the rings first and redone from scratch?
To save yourself some trouble keeping the rings aligned to the scope, loosen one at a time on the scope. With the rail screws loose (obviously) you can then adjust the loose ring to where you want it, tighten it to the rail, then tighten to the scope.
If you need to move the other ring, just repeat the process.