Liat, out of the box JSD comes with a "Transition on comment" automation for status Waiting on Support and Waiting on Customer. If that is in place then you should be able to edit this automation simply adding your statuses. If not in place then it is a simple matter to create.
Basically it looks like this:
Add a new rule selecting "When comment added" then edit from there....
When: Comment added
If: Issue matches Status = "Waiting for reporter"
Then: Transition issue "Waiting for support"
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