The correct option is A Even though
In the sentence, there are two clauses "My old teacher gave ...money" and "he was poor", because both have a subject and a verb in order to make them a clause.
Option D: 'In spite of' is a preposition, followed by either a noun or a gerund (eg., 'in spite of his poverty'). It does not connect the clauses, hence the underlined words must be changed. So, option D is incorrect.
Option A: The meaning of 'in spite of' and 'even though' are the same, both refer to contrast. They mean 'despite the fact that'. But, the latter is a conjunction that connects two clauses.
Hence 'even though' must replace the underlined part and A is correct.
Option B: 'As if' refers to manner, it means 'in such a way that it seems to be true'. For example, 'she spoke as if she knew the entire matter, even though she didn't'. It isn't relevant here, as the sentence refers to contrast. Hence B is incorrect.
Option C: 'However' refers to contradiction, it means 'but', whereas 'even though' means 'in spite of the fact that'. If 'however' is placed here, the form of the sentence would have to change. Hence C is incorrect.