Moving from Saitama to Tokyo, Will the health insurance I paid for this week be valid?

I am moving from Saitama to Tokyo in about 2 weeks. I have 4 months of health insurance bills I want to pay off (for Sept, Oct, Nov, and Dec, but in the midst of the move I might lose them SOMETIME if I wait). If I pay while I'm still a resident of Saitama, will they still be valid when I become a resident of Tokyo? Will it cause any problems for me if I pay now? Does health insurance cost different depending on the prefecture?
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Please tell me what kind of insurance that is. Are you talking about National Health Insurance? If so, the premium you paid is valid no matter where you move. But you need to go to shiyakusho and change the address of your insurance. >Does health insurance cost different depending on the prefecture? There is only SLIGHT difference.
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