(S is a proper class wrt model M) implies ((|T|=|S| under model N) implies (T is a proper class wrt M)). Why?

Question

If I understand correctly (which is far from guaranteed, so a reply telling me that it is rubbish will be better than no reply at all):
Suppose we have two models N and M such that N is a (non-conservative) extension of M, such that the class S is a set under N but not under M, with respect to which S is a proper class. Then we can talk about the cardinality of S (having it understood that we are working under N). So, if we have such a class S, and another class T which is a set under N such that |S|=|T|, then T is also a proper class with respect to M.
Questions: Correct? If not, please point out where and why. If so, why? Thanks in advance.