Yes and no
So, the DG2813 and 4813 have the dial feet in the same place. The stem height is the same. The hand sizes are the same. Therefore, it should be a direct swap.
However, like the ETA family of movements, they come with different length pinions. Almost all DG4813s seem to have the low hand stack, so many times when you do the swap, everything fits until you go to install the hands then you find that there's not enough clearance between the hands and the dial.
There used to be high-hand-stack 4813s, but the supply seems to have dried up.