Typically a Bill of Sale or Assignment will do it. In fact, many share certificates have transfer language on the reverse side of the certificate. If indeed you have a certificate.
No I do not think you will need to close and start over for this narrow purpose.
More importantly, though, please consider the tax implications as well as transfer restrictions. Meaning, if your business has any secured debt outstanding, transfer of your shares may well be an event of default.
There are a number of different ways to accomplish the transfer of the company. You can simply sell all of your shares to our husband. He then becomes the owner of 100% of the shares. You can sell the assets of the company to him. This may be best if there are some liabilities of the company that need to be dealt with. The sales price and terms could be important especially depending on whether the assets are mainly depreciated or whether there are capital gains issues. There are situations where closing the company and opening a new business may protect you more than selling the business or stock to your husband.
It is difficult to say what would be best for you and your husband without more facts. Practically, you probably do not need to worry too much about the process if the company is really small and has little value. However, you need to talk to an attorney and CPA if the company has substantial value.
Good luck.
