perfect

Instead of “on behalf of him” you can say, “on his behalf.”
“On behalf of” is a little formal, so it might not work in the sense of a birthday party.

“We would always hitch a ride traveling” … if you mean that you would ask strangers to take you from place to place, you would say, “My friends and I would always hitchhike on vacation.”

Hitch a ride is with someone you know, or on a scheduled route. Hitchhike is to go out on the highway and hope a stranger takes you in the right direction.

The “your” and “he” are confusing me a little. This could work, but doesn’t seem natural.

That might be because of a small detail. If you start a sentence with “On behalf of…” we typically make a statement to a person that comes from a group. So you would say, “On behalf of your colleagues, we wish you the very best for your retirement.” Or, “On behalf of the whole company, we thank you for your years of service.”

However, if you’re talking about something else that happened, you put the thing (or statement) first and “on behalf of” second. So here you might say, “He gave a moving speech at the graduation party on behalf of all the employees of the company.”