Can the client punch in a code on the phone that would indicate their Author ID or Name, etc

Yes, the LFH-9850 does support Author ID’s. This allows authorized phone recording only. Up to 20 Author IDs can be assigned to 1 Desktop 9850. You can also grant advanced user rights as well (which means full remote functions will be available to them.).
Page 15 of the Digital Telephone Desktop 9850 manual will show you how to assign author ID’s.