The use of "for" in a sentence
Solution 1:
I think either the entire sentence is erroneous, or has clauses which are redundant.
This research work is in debt to the parents and husband of the author x; father, mother, and husband, for their help to fund her Ph.D studies, she could develop this idea and complete this work.
In the above passage, the first sentence already limns that the research work is for her parents and her husband. The sentence after the semicolon again mentions the same people, which is redundant.
I'd eliminate the semicolon, and make the sentence much more succinct, as follows:
This research work is in debt to the parents and husband of the author x, with whose funding for her Ph.D, she could develop this idea and complete this work.