I wrote him a letter explaining the reasons. vs ...the reasons to him.

[Hanifasmm]

Hi everybody,
Are the following sentences correct?
1. I wrote him a letter explaining the reasons.
1a. I wrote a letter explaining the reasons to him.
2. I wrote him a letter to explain the reasons.
2a. I wrote a letter to explain the reasons to him.
If wrong, could you please explain the grammatical error involved.
Thanks,
Er.S.M.M.Hanifa

[Kitosdad]

All would appear acceptable.
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[Hanifasmm]

Mr.Kitosdad,
Thanks for the prompt reply.
Could I shorten the above sentences as below?
1. I wrote him explaining the reasons.
1a. I wrote to him explaining the reasons.
2. I wrote him to explain the reasons.
2a. I wrote to him to explain the reasons.

Thanks,
Er.S.M.M.Hanifa