+1 to everything that importer has responded with.
To add, if you are serious about doing this - and on the basis that you have no formal shareholders agreement, it might be best to consult a lawyer as well as an accountant.
You can inform or discuss with your partner that you are going to do this and that you would like to draw up an agreement to sign over over the share to them.
Doing that - would all hell may brake loose, or do you think your partner would be OK formalizing an agreement for the sale of shares to them or a third party.
Does your partner have the money to buy the shares, if not have you considered an alternative approach - is there someone you know would buy the shares, possibly one or more of your employees?
Moving to the next stage - after you have decided what the value is in your mind - you need to discuss and decide between you and your partner what the value of the shares are worth, that is fair and equitable.
Generally a small business started between two people where they each put an equal amount of money in - this may be the limit of what your shares would be worth today given the fact that the business is not making a lot of money.
Is the business net profitable after all other costs? - make sure you do not confuse gross revenue to net revenue.
It also depends on any assets that are present at the date that is chosen to sell your shares over, such as the net cash balance, inventory, any equipment at book value or any goodwill - such as a client base or any ongoing reoccurring revenue income.
Somewhere there must be bank statements, income and outgoing ledgers or spreadsheets, taxes paid, utility bills that shows this as an established business.
A general comment for anyone else looking at this post - If you have been running a sideline business out of your own homes with little to show in the way of a formal business and without business records or bank statements (similar to a sole propriety business operation), then you may have a sticky situation with regard to value.
On that point I'm thinking something such as an ebay type buy and sell trading business, a service business or something that does not require inventory or equipment such as a software or consulting business.
Ask yourself - are the shares really worth anything, or if there is anything of any value currently or ongoing.
What if either you or your partner simply walked away today - would there be any tangible value, or would the person left running the business be left with value or debt
Trust this helps and good luck