How Do I Confirm An Address Change?

I had a sears card many moons ago. I got divorced and moved across country. Ten years later I applied for another sears card, was approved but sears keeps sending my statements and I think my first card to the ex-wife's address. I called customer service from a store to change the address but my most recent statement still has the billing address wrong. I need to make sure once and for all that the address has been changed!