I look at the issue differently. You have been appointed to handle HR operations for the SBU that has operations in India. In that case, when you were appointed, your Director should have immediately sent a proper business letter to the existing HR Manager about what he should hand over, when he should hand over, by what date he should hand over, what knowledge transfer he should do, etc. Since your Director has not done this, you have taken over his work on your shoulders and now wish to write an email to the existing HR Manager. Who should do what type of work, when they will do it, and where they will do it is always decided by the top management and not by lower management.
The major issue that I find is that your Director has not understood two important things. One is the medium of communication. After telling your counterpart verbally, he should have sent the written letter. In this letter, he should have asked to forward handing/taking over a report by a specific date. The second thing is that your Director is wary of exercising his authority. Your counterpart has defied the Director's authority. How come an HR manager, a paid employee, mustered the courage to do that?
It appears to me that when you were appointed, well before your appointment, the Director did not take into confidence your counterpart. Today, what he is doing is nothing but living in the world of denial. This denial has resulted in resistance to change. Change is on account of the appointment of a new HR Manager that forces him to partake in his authority.
The problem also lies with today's work culture where there is too much reliance on oral communication and less on written communication. A written order on the company's letterhead to transfer the charge would have made a big difference, and your counterpart would have been less defiant than he is today.
If you have not sent the mail, then I recommend speaking to the Director and sending the existing HR Manager a proper letter to complete the handing/taking over process. It is better to shoot by keeping a gun on someone else's shoulder. Sending mail for the transfer of change, however polite it might be, is tantamount to taking the gun from the Director's shoulder to your own shoulder. Gentlemen, never do that!
Thanks,
Regards, Dinesh Divekar