In a lengthy court battle, the judge decided that the woman’s ex-husba

Decided is a subjunctive verb and hence will be followed by 'that'
So, we can eliminate C, D and E.

Options left:

(A) that the woman’s ex-husband remained indebted to her for the property

(B) that the woman’s ex-husband remained indebted to her because of the property

Now, we have to decide between 'for' and 'because':

The distinction between the two, 'for' and 'because', is just about lost to native speakers.

Let us understand from examples:

1. She was crying, for her mother was seriously ill.
and
2. She was crying because her mother was seriously ill.

The use of 'because' introduces the subordinate clause that gives the reason she was crying.

In contrast, 'for' is used as a coordinating conjunction to stress that both pieces of information are of equal importance:
'she was crying' ' and 'the mother was seriously ill'. In (2), the 'because' version, it is 'she was crying' which is stressed, of major importance, and the reason why is then added on.

"I trust him, for he is an honourable man." stresses that 'I trust him" and separately, quite apart from whether I happen to trust him or not, 'this is an honourable man.'

To say, "I trust him because he is an honourable man" indicates that 'I trust him" and the 'because' clause is subordinate to that, merely explaining the basis for my 'trust'.

As we understand from above examples, we should have 'for' in the right answer.

Hence, answer should be A.