Nick, you didn't give your age or length of service. I'd see if there is a forum specifically for Federal service employees somewhere to ask? I did find this:

Former Employees

I kind of doubt you can re-invest, probably just "start over" with this new job. But if you think you are going to be leaving this job soon, I'd just invest what you were paid out and make your own annuity/401 sort of account; "roll it over" in some way in other words.