How can a sub-landlord transfer his security deposit refund to a sublessor?

It is not that complicated. You need a letter signed by him instructing you to give his refund money to the woman. It should also state that he is giving up any claim to the deposit you are holding. That doent will hold up in court. You are not putting yourself at risk of a future lawsuit. Hold onto that letter for several years for your own protection. It should also be notarized.