If it's an exam and there's no space for comments, I would definitely put "him."
Having said that, there are some cases when it could be "his" such as in the following dialogue:
"There are three cats in the waiting room. Two are with a woman who has been waiting since 10 o'clock. The other is with a man who just rushed in and has to catch a plane in one hour."
"Let his come in."
Here we are distinguishing between her cats and his cat and it is very clear what is being said.