Let his/him know

Hi everybody! Few days ago my mate attended to a job competition for a job in the technical office of Rome. Among the many legal questions there were also some English questions. The one I am asking your help for is:

“Let ……. come in.”

the possible answers proposed are:

- his

- him

- he

I am sure that all of you are thinking that the only right option to chose is “him”, that’s it.

Initially it was confirmed “his” with correct answer and after few days was corrected with “him”.

The english questions/phrases put in these competitions are generally extracted form bigger pieces, books.. and my partner didn’t answer because he says that in a certain contests it can be also right “Let his come in”, for example:

Michele is waiting for the vet to visit his cat. When the vet wants to visit Michele’s cat can say to his secretary:

<< Let his come in >> instead of << Let his cat come in>>.

What do you think? Is it possible consider both the options “his” and “him” correct?
Have you read some examples in books or articles in which you have found the phrase “Let his come in” ?

It can help my partner to obtain the job because he got a score of 20.8 and he had to get 21 to obtain the job! So it is very important the help of all of you.

Thanks !!!!!!!!!