These two items may be one and the same. Magus's Amulet came from Schala; she gave it to him before the Ocean Palace Incident, and he kept it throughout his life. Meanwhile, the Astral Amulet is a mysterious artifact from Zeal possessed by Lucca and given to Kid during her infancy. It consists of a piece of wood tucked in a purple pouch bearing the Zeal crest in gold and black. Now, consider that Cross's backstory was probably fleshed out before they decided to axe Guile's backstory as Magus. Is it plausible that Magus's amulet is the Astral Amulet, and that Magus, having knowledge of Project Kid or simply of Kid's existence, visited Lucca and gave Kid the amulet for her own safety?
This possibility would not only explain the mysterious origins of the Astral Amulet, including its crest bearing the Zeal emblem, but would also neatly link the mysterious item with established Chrono canon. Thematically, it is also interesting to see Magus give the Amulet back to his sister (albeit in a different form).
What do you think? It's a possibility, and even tantalizing, since it gives Magus a better chance at knowing what happened to his sister. Lucca's letter doesn't support or refute this much, but Lucca's speaking to him as the very personal Janus may imply that they became closer friends (and that the letter was written much later after 1004 A.D., which would be likely since she had to have had met Luccia by its writing). I'm not one to assume Magus or cool characters is behind every unexplained action, but the pieces seem to fit here. We won't ever know for sure, but it is a fun possibility.