When to add a coauthor to a paper I am working on?
First, yes, you should speak with him. There different ways how to approach him and I would suggest to inform him about your progress (something you should do anyway) and to just ask him how to proceed regarding co-authorship.

In general, merely posing a conjecture does not merit co-authorship, but you could ask, if he would like to contribute to the paper (e.g. by checking/rewriting the proof/statement of the conjecture, providing more intuition as to why this conjecture is true, putting the conjecture in context with references…).