(a) A person becomes a limited partner on the later of:
(1) The date the original certificate of limited partnership is filed; or
(2) The date stated in the records of the limited partnership as the date that person becomes a limited partner.
(b) After the filing of a limited partnership's original certificate of limited partnership, a person may be admitted as an additional limited partner:
(1) In the case of a person acquiring a partnership interest directly from the limited partnership, upon the compliance with the partnership agreement or, if the partnership agreement does not so provide, upon the written consent of all partners; and
(2) In the case of an assignee of a partnership interest of a partner who has the power, as provided in section forty- two of this article, to grant the assignee the right to become a limited partner, upon the exercise of that power and compliance with any conditions limiting the grant or exercise of that power.