Memory was of imperative cultural importance in Archaic Greece, since it was linked with the afterlife and immortality. The primary factor that motivated Achaean heroes such as Achilles, kleos or glory (literally "being talked about"), was coveted, because doing glorious deeds was the best way to be remembered. If a hero is remembered, then they can never die, because their deeds live on in the memories of others.
This touches on one of the central themes of The Song of Achilles, which is Achilles's constant liminality between hero and villain, lover and soldier, mortal and immortal. Throughout his life as a demigod, Achilles is trapped in between the mortality of his father and his immortal maternal heritage.
This liminal state is reflected in his afterlife as well. As a mortal, he is destined to die and descend to the underworld. As a demigod, he attains immortality through the memory of his great accomplishments that will be forever recorded in literature like Homer's Iliad and Miller's The Song of Achilles.
When Patroclus says he is "made of memories," he too is in a liminal state between death and the underworld, unable to move onto the next life because he not been given the correct burial rites. Having already physically died, in one sense, Patroclus is quite literally made of memories, because it is only our shared remembrance of his life that gives him substance. However, this could also be interpreted as Patroclus doing his part to keep Achilles alive through remembering their shared experiences.