Here are the rewritten sentences:

1. Although he has a very important job, he isn’t particularly well-paid.
**In spite of** his very important job, he isn’t particularly well-paid.

2. Although I had never seen her before, I recognized her from a photograph.
**Despite** having never seen her before, I recognized her from a photograph.

3. We thought we’d better invite them to the party although we don’t like them very much.
**Despite** not liking them very much, we thought we’d better invite them to the party.

4. Although I didn’t speak the language, I managed to make myself understand.
**In spite of** not speaking the language, I managed to make myself understood.