Finish strong. Rest up. Towards the end of July, plan on ways that you can hit the ground running in the fall. Potential tasks include:
reading up on the policies of your new program and school,
making sure that the i's are dotted and the t's are crossed with what ever financial support you're receiving,
doing background research on the professors with whom you will likely work,
identifying and reading one or two "must reads" in your intended fields (don't over do it),
revisiting your notes/work from your UGI so that you know what you're supposed to know, and
developing an understanding of the differences between being an undergraduate and a graduate student.
It gets confusing with the names of all the exams (proposal defense, quals, comps, prelims, etc.). I had my proposal defense, and was successful - so my prelims were waived, especially since I've already completed a Masters program. But I still have comps next term, and then my final dissertation defense in 2019. Plus, I already did one proposal defense before I switched advisors/projects, so this was my second one and was vastly more "informal" than the first. But I think, in a way, that yes, it is helping me prepare because I got a lot of good feedback about potential formats and ideas for my comps during my proposal defense. But I suppose we'll see when I do my comps next term. :-/