Thanking him for doing legwork IS GOOD. My DB coach said to "applaud loudly for the 1% positives they do" and it does help.
25years, I disagree with this as it pertains to the initiation of separation. Why would we want to applaud our spouses ripping our hearts apart by moving out, turning our lives upside down, canceling utilities, taking furniture, etc?
We can applaud the positive actions/behaviors which will, hopefully, generate more positive responses. This is called 'positive reinforcement' for a good reason! Not too different from dog training or potty training!
Suffice to say, I think it is just plain good manners and courteous to acknowledge H's email and thank him for it. Nothing less, nothing more. We don't need to do hand springs here.