What is the difference between 一ヶ月間「に」いい思い出になりますように願っています。 and 一ヶ月間「が」いい思い出になりますように願っています。 ?Feel free to just provide example sentences.

一ヶ月間 is same as 一ヶ月の間.
一ヶ月間 means a length of one month, so 一ヶ月間に can be translated as "in/within a length of one month".

一ヶ月の間 means "during a length of one month", so 一ヶ月の間に can also be translated as "during a length of one month".

Your composition of using 「に」, with no doubt, makes sense.

In this expression, there must be something which becomes いい思い出 within the period of one month. Length of one month with every experiences is not the object for いい思い出になる.


一ヶ月間「が」いい思い出になりますように願っています。
This expression is telling that length of one month with every experiences is expected to become いい思い出 because が as particle for subject supports 一ヶ月間 so that 一ヶ月間 itself is to become いい思い出.