All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
It is forbidden to charge stud fees for a stallion because it was narrated that (Abu Hurairah) said: "The Messenger of Allah forbade the price of a dog and stud fees for a stallion." {Related by Bukhari}.
However, it is permissible to lend the stallion for such purpose and Allah will reward the owner for that.
Similarly, if the owner of the mare gave the owner of the stallion some money as a present, then-we hope-that this is permissible. And Allah The Almighty Knows Best.