Hi. Can you kindly elaborate on which option can be correct and why? ( much obliged in advance )

Mr. Hill decided to offer the position to Henry, ………… .

1. Having rejected his job offer by Bill
2. Bill having rejected his job offer
3. Bill rejecting his offer
4. Being rejected his offer by Bill

I think 2 is the only one that completes the sentence properly. Hard to explain why, all I'll say is that the continuous form of the verb 'to have' (i.e. 'having') gives a sense of Bill's decision continuing to have some current relevance, while the past form of the verb 'to reject' (i.e. 'rejected') conveys the fact the decision was made in the past. Hmmm.

It's 2. It's clumsily worded but it's the one which makes sense and isn't a dangling modifier.