He probably paid Iran a sizable fee and promised to let some of their leaders on the yacht with the sex slaves he has acquired.

He has ongoing bribes going Trump's way as a matter of business.

Plenty of ships pass the strait and this is kind of to be expected. Especially the UAE, but also other Gulf countries have been key places for money laundering. They allow Russians in and do not ask many questions. Mordashov also probably has contacts to Iran, so he can make these sort of deals.