There is an inconsistency in your question. You are asking about adding a shareholder to an LLC, but LLC's do not have shareholders. They have members. They operate without stock and without boards of directors. Form 2553 is used to create an S corporation. One creates a garden variety corporation under state law, and then files the Form 2553 to establish the S corp status. It is possible to qualify an LLC to be taxed as an S corp, but it is really redundant in the main--sort of like wearing a belt and suspenders.
If you have a corporation, you simply issue stock to your new shareholder. If you have authorized but unissued shares, you can issue some or all of them, depending on what percentage ownership you are giving. If necessary, you can authorize more shares and issue those. That addition of shares though will likely require an amendment of your articles of incorporation.
If you have an LLC, you simply add the new person as a member and modify your operating agreement. It would be prudent to assign the membership interest in a formal document and recite the consideration given for the interest.