She let us know the truth behind the murder of her friend.

Can I replace 'her friend' with him? (Given that I have already mentioned the name of the victim)
No, you cannot use the objective pronoun as the object of the preposition. You can do this:

She let us know the truth behind his murder.
Thank you.

You have been most helpful to me.

Do you have a list of prepositions as reference? Can I have it?
Teachers: We supply a list of EFL job vacancies
You are welcome among us.

Is this wrong? Us is a subjective pronoun. Among is a preposition.
It is not wrong ('us' is an object pronoun).

To make my earlier statement clearer: you cannot use the objective pronoun as the object of the preposition 'of'. 'The murder of her friend' is OK. 'Her friend's murder' is OK. 'Her murder' is OK. 'The murder of her' is not possible.
Site Hint: Check out our list of pronunciation videos.
So, it applies only to 'of'?

I made it for her.

I named my son after him.

I am responsible of (it).

The first two are correct, the last one is wrong. Am I correct?
So, it applies only to 'of'?- I'm not sure. Probably only where 'of + object pronoun' is the equivalent of the possessive pronoun ( e.g. where 'of us' = 'our')

I made it for her.

I named my son after him.

I am responsible for it.

The first two are correct, the last one is wrong. Am I correct?-- The last one is wrong, but for a different reason. I have fixed it.

This is my suitcase.-- Good

This is the suitcase of me. -- No good. 'Of me' = 'my'.

He is afraid of me.-- Good

They are in charge of me.-- Good

For the life of me, I cannot understand Japanese.-- Good. 'For the life of me' is an idiomatic phrase.