In the following reaction there are three possible aryl groups that can migrate: an unsubstituted phenyl group, a p-methoxyphenyl group, and a p-nitrophenyl group:
Why does the electron-rich p-methoxyphenyl group migrate instead of the phenyl or p-nitrophenyl group, especially when it leads to a carbocation that is less stabilised (since it will no longer be conjugated with the stabilising p-methoxyphenyl group, cf. the crossed-out arrow)?

