Hi! I don't think that there is a migration tool. The two tools are just too different. But you can integrate your QTP-Scripts by using the test type "Generic Test" in Visual Studio or Test Center. A Generic Test is a wrapper for existing tests. You can specify an executable file, arguments, environment variables, the working directory and also the location and name of the result file.
Yeah... your organization will need to be licensed in order to execute QTP test cases through any tool, including Microsoft's Visual Studio and / or Test Manager. I don't think you can stop paying for QTP and expect to be able to use it indefinitely.
Based on past experiences with different software companies, I think that at some point, your license will expire and HP will probably charge you a boatload of money to get back on support and resolve your license issue. After all, your organization isn't really paying for the software; it is just paying for the right to use it. So the moral of the story is to not walk away from the current system until your organization is absolutely positive that it can live without it.
Go to your QTP License Manager to see when it expires (if you have a floating license). Usually there is no expiration to use the tool (as long as the license managager is remains on the same server), but your support sure does expire. Mine support expired for about 6 months and I was still able to execute scripts.