Amaleki retained the small plates from the time he and other Nephites fled the city of Nephi through the seating of Mosiah1 as king, and through Mosiah1’s death and the seating of his son, Benjamin. The small plates do not end with the arrival in Zarahemla, but rather when Amaleki “began to be old.”
In verse 30 Amaleki will note that the plates are full. When he gave the small plates to Benjamin it was a combination of factors. Amaleki had no sons, and perhaps no brother, to whom the plates could be given. That, combined with the physical end of room on the plates, convinced him to complete that record and give it to king Benjamin.
Amaleki understands that the small plates were for the things of the ministry, and, therefore, he declares his faithfulness to the gospel, and to Benjamin’s faithfulness. This fulfilled the purpose, and also passed them along to a righteous successor.