We have a sole proprietorship business. Husband is retired and collecting social security. How can wife take over the business?

I don't recommend filing separately because you lose several important benefits of filing jointly. If business is a sole proprietorship, it could be as easy as incorporating the business in wife's name with your department of state. Consult with a business attorney to set up said entity.

The easiest way would be to make a new business (maybe an LLC?) that is just under your name.