assign the copyright to you -- an "all rights" agreement typically means that all of the rights to a book or artwork or music are assigned permanently for a lump sum payment -- you can file an application to register the copyright as owner. In the application, you would list the family friend as author of the work and list yourself as owner (or "copyright claimant"). During the application process, you will see a statement " If any claimant is not an author, you must include a transfer statement ..." (a shot from the online application process is shown below), and you would choose "By written agreement" from the drop down choices.
Recording the assignment. In addition to registering the work, you can also record the assignment agreement with the Copyright Office. It's not necessary but it makes the document available for public inspection and can help establish priority of ownership rights if there is a dispute. The procedures for recording transfers are explained in this circular.