In other words.....there's no reason to plead the 5th....unless of course that it may incriminate "someone else"
You have no fifth amendment right to protect another person with your silence.
If given immunity such that your testimony cannot be used at all against you , your fifth amendment right is fulfilled by this immunity, but this immunity is lost if the testimony thus given is silent or false.
If this guy has a lawyer ,the lawyer needs to tell him better how this works.