***** NOT A TEACHER *****
Hello, Yura Reiri:
(1) Let's analyze your sentence : I + wrote + a letter + to him.
(a) You are 100% correct, most books (not all) say that there is
NO indirect object in your sentence. "To him" is a prepositional
phrase ("to" is the preposition; "him" is the object of the preposition
"to"). The prepositional phrase modifies/ refers to/ belongs to the
What did you write? A letter (the direct object).
To whom did you write the letter? To him (a prepositional phrase that
modifies the verb "write").
NOTE: Yes, some teachers want to make this matter easier, so they
call "to him" the indirect object, but most books and teachers do NOT.
On a test, you must, of course, give the teacher the answers that he
I wrote him a letter. Now you have a real indirect object: him.
Remember that a real indirect object does NOT follow a preposition.
Many times (NOT always) you have a choice: a real indirect object
or a prepositional phrase:
I baked Mona a cake./ I baked a cake for Mona.
I sent Mona some flowers. / I sent some flowers to Mona.
I asked Mona a question./ I asked a question of Mona.
P.S. If you do not understand my answer, just start a new
thread (with another example sentence). There are some
wonderful teachers and non-teachers here who can answer
your question better than I.