"On receipt of the initial registration fee, the above statement and the accompanying certificates in respect of each general partner, the Registrar will register the exempted limited partnership and issue a certificate of registration to the general partner."
See Establishing an Exempted Limited Partnership athttp://www.ogier.com/publications/library/pages/Establishing_an_Exempted_Limited_Partnership_in_the_Cayman_Islands.aspx
A Certificate of Registration from the registrar of exempted limited partnerships would be legal proof that a company has that status.
The above link also states:
The partnership agreement normally provides a procedure for admitting additional or replacement limited partners which is likely to involve the new limited partner executing a deed of admission in terms of which it agrees to be bound by the terms of the partnership agreement and pursuant to which it grants any power of attorney
contained within the partnership agreement to the general partner. As such, the deed of admission must be executed as a deed. In addition, each of the existing partners must consent to the admission of a new partner. Procedurally, consent is normally provided by the general partner counter-signing the deed of admission for itself and, acting on the basis of the power of attorney granted to it in the partnership agreement, on behalf of each limited partner.
There is a Guide to Exempted Limited Partnerships posted here
If you need more detailed information, you may wish to consult one of the business formation attorneys in the Caymans listed by location here
I hope this information is helpful.