Noun clauses of this variety, sometimes called "embedded yes/no questions,"
appear in many nominal positions:

subjects

Whether he will remember me is an open question.

"extraposed" subjects

It is an open question whether he will remember me.

objects/complements of prepositions

I am concerned about whether he will remember me.

as well as complements to verbs, as in the sentenence you gave,

I wonder [whether] [if] he will remember me.



 What type of construction follows "I wonder"?  For example:
>
> I wonder if he will remember me.
>
> The clause appears to be subordinate, but it certainly isn't prototypical:
> It cannot be moved, and it appears to be functioning nominally, an option I
> didn't think was available to subordinate clauses.
>
> Thanks in advance,
> John
>
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