Delving a long way back into my memory banks, I made a couple of bits for someone with a Unimat. Certainly the mounting thread on the Tailstock was 12 x 1, (Still have the Taps ) and so was that on the mandrel. But it was in the dim and distant past.
So it is very likely that the 50 mm chuck will need a backplate to suit it.
At the risk of teaching granny to suck eggs, Once the backplate has been threaded 12 x 1, with a register to suit the Mandrel, the O D should be turned down to provide a really snug fitting register in the chuck
In this way, you will produce a register on the backplate which is as concentric as possible to the Mandrel, so that the chuck runs as concentric as possible.
If it is a 3 jaw, it will not hold work absolutely concentric. Do not be surprised at a run out of 0.075 mm. Such things do happen. If you need to have two ( or more ) diameters absolutely concentric, they have to be produced without disturbing the work in the chuck while each diameter is turned.
HTH
Howard