Can a round diamond be re-cut to princess diamond?

I received a princess cut engagement ring. My mother wants to give me the diamonds from her wedding band to put in my wedding band and my fiance’s wedding band. I would like all the stones to be the same shape – princess. Is this possible?

Yes
Unless there are all sorts of flaws in the stone, a good jeweler should be able to make it into a princess cut, however, it will be smaller after it is cut