The principles of both teams need to work together to establish a transition plan so that everyone is crystal clear on how to answer the who, what, where, when, why, and how the transition will work. I would bet the three biggest risks you will face is a severely constrained timeline in which to conduct the transition, stakeholder grief due to the imminent degradation of support services that WILL occur because of the transition, and the new team not have all and/or the right resources--human and otherwise--ready to go.
Is this change due to a re-compete loss? If so, the new team should expect a transition partner that might range from what looks like lazy to downright sabotage.
I think having a readiness checklist is critical, and it should be derived from the plan above. You might use the risk breakdown structure to help brainstorm those things that need to be on the checklist: Technical, Security, Equipment, External, Financial, Organizational, Contractual....
If I had to choose the highest priority in the change, it would be the impacted stakeholders, the teams' customers, creating early and ongoing communication setting the expectation that services will be less than desirable for time to come. These would be the highest priority risks on which I would focus during and after the transition.