1. He called me later.

2. He rang me back.
3. He gave me a ring back.
4. He telephoned me back.
5. He made a phone call to me back.
6. He gave a phone call to me back.
7. He made a call to me back.
8. He made a call for me back.
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(I have wrtten several expressions. Which ones are ungrammatical? Which ones are commonly used? Thank you. Do you have some more useful expressions?)

1 through 4 are all just fine. 5-8 are not. They are awkward and would cause your reader or listener to stop and think, "What does he mean?" :) Grammatical or not, they don't work.