If the second member is coming on board, and if he is an employee no problem
Other wise, there is a new business, a partnership (or maybe an s-corporation if that election is desired) with a written partnership agreement registered with the state and the IRS - a new FEIN is also required. LLC does not change this requirement, it is a state only designation.
With only two months into a sole proprietorship, if it were me I would create the partnership agreement as of the date the business began. Backdating is iffy and technically wrong though. I do not know if you would run into issues with the state or the IRS for filing the partnership paperwork over two months late.
And a sales tax permit issue as a sole proprietor would have to be closed and reopened under the partnership name.
I suggest you get with a tax accountant and lay this out for him.
From what you say, technically, the first member would close the business, reporting a short tax year and that signing bonus is income.
Then the partnership is formed with each member contribution equity.