(a) A foreign limited liability company may amend its application for authority from time to time if the amendments contain only such provisions as might be lawfully contained in an application for authority at the time of making such amendment. To accomplish such amendment, a certificate, entitled "Certificate of amendment of ... (name of foreign limited liability company) under section eight hundred four of the Limited Liability Company Law," shall be signed by an authorized person and delivered to the department of state. The certificate shall set forth:

1. (1) the name of the foreign limited liability company as it appears on the index of names of existing domestic and authorized foreign limited liability companies of any type or kind in the department of state, and the fictitious name, if any, the foreign limited liability company has agreed to use in this state pursuant to section eight hundred two of this article;
2. (2) the jurisdiction of its organization;
3. (3) the date it was authorized to do business in this state;
4. (4) each amendment effected thereby; and
5. (5) if the true name of the foreign limited liability company is to be changed, a statement that the change of name has been effected under the laws of the jurisdiction of its formation and the date the change was so effected.