Having seen similar discussions many times my advice would always be to start by checking there is no play in the headstock bearings – put an indicator on the bar near the chuck and pull the far end around with modest force. A small amount of movement may be acceptable, especially with plain bearing lathes.
Now with the lathe unstressed and unadjusted with the headstock end of the bed firmly fixed down and the tailstock end with fixings no more than hand tight.
Then use 'rollies dads method' which is ideal for a decent bar held in a chuck. (google will bring up a very clear pdf on how to do this, it's not unique to Rollies dad, but that has become the de facto name for the process.)
Packing the near or far headstock foot shoudl be enough to get everything perfick, if required.
If you want to tighten up the tailstock bolts, repeat the test and you will probably need to add or remove packing.
If the lathe was aligned in its old home, this should be able to sort it.
Because it measures the actual alignment of the spindle rather than a proxy (bed being level) it is more accurate.
As you have moved the headstock, all bets are now off and you may need to move it again if it is now too far out of whack.
Neil