The following question is to be put into reported speech:
"Shall I ask her out for a meal?"
He has has been wondering whether to ask her out for a meal.
How do I go on if the sentence starts like this:
He has has been wondering whether he ......
Is it "shall / is to / is supposed to / should /was to / was supposed to ?
I'd prefer "should" but I may be wrong.
What do you suggest?
You are right, should is OK.
I would say it this way:
He was wondering whether he should ask her out for a meal.