Can I use the past perfect with present perfect in English

Solution 1:

There are some common combinations of tense constructions in consecutive clauses. But there is no rule that prohibits the past perfect in a clause following a clause containing a present perfect. Indeed, just about any consecutive clauses can contain any verb construction.

In your case, the most likely context suggests the present perfect in both clauses:

He has informed me that you have approved his request for a loan.

But the past perfect is feasible in the following context:

He has informed me that you had approved his request for a loan, but changed your mind the following day.

This is a typical use of the past perfect to indicate the past in the past.