Do not drop your current insurance until you have a new plan.
I am not sure but I do not think preexisting conditions should be a problem since you currently have insurance. I think you can get a letter from the current company that you are covered and you give that to your new carrier. I would check with your HR department. You could also call your current company and tell them you are moving and want to get a personnel plan similar to what you have for that location. They might be able to help you.
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