The Cosmic Sword S is misnamed in the English localization of Strikers. This is due to how in the original Japanese, the Cosmic Sword S is called the CS Replica, and two of Morgana's weapons share this acronym: this weapon, and the actual weapon the Cosmic Sword S is supposed to be, Claimh Solais.
Several points to support it:
The Cosmic Sword S doesn't resemble how the original Cosmic Sword looked like, but instead resembles how Claimh Solais resembles.
The CS Replica has the exact same effect Claimh Solais has, that being raising Morgana's Max SP while equipped.
Allofthestrongestmeleeweapons that the original Phantom Thieves wielded are in Strikers during the endgame, and Claimh Solais was Morgana's strongest blade.