grammar - Is it correct to use "his" in this prepositional phrase?

In this chat message I was attempting to say that I was installing Ubuntu on a friends laptop. What I wrote was,

I had a friend for whom I installed Ubuntu on his laptop.

Grammatically, it seems like it works: if I switch around the sentence a bit, I would still use the same kind of prepositional phrase:

I installed Ubuntu on a friend's laptop for him.

Also, if I simply replace the his for an a, it sounds right:

I had a friend for whom I installed Ubuntu on a laptop.

However, how I initially wrote it, it doesn't sound right. Is what I wrote initially correct, and if not, why not?

Answer

All of the examples given are correct, though they differ slightly in meaning.

In the first two, the use of "his" indicates that the laptop belongs to the friend (and that the friend is male).

In the last example, the use of "a" just indicates that you did your friend a favor by installing Ubuntu on a laptop. It does not specify whether the laptop belongs to the friend or not, nor does it imply the gender of the friend.