This is a Persona 5 Guide on where to find all the treasure demons in Memento and how to recruit them.
To find them more easily you can craft an infiltration tool called Treasure Trap. It does work in Memento (I tried, and Memento is a public Palace anyway) and it increases their spawn rate.
The process of recruiting is actually really easy. Only one of them is immune to physical attacks (Stone of Scone, which is weak to curse) so you just need to bring a Persona with a high critical skill and one with a curse skill (lower level is better so you don't kill the enemy)
The personas I use in this video are:
Hanuman (64/Star) with Revolution (increases crit rate for everyone for 3 turns)
Koppa Tengu from fusing Obaryion (Lucky Punch) + Andras (Apt Pupil). Lucky Punch has high critical rate and Apt Pupil increases critical rate of your physical attacks.
Agathion for weak curse damage (Eiha).
If you already have Regent, you can itemize it for medium critical rate up accessory.
List of Treasure Demons in Memento
Regent (10/Emperor) in Path of Aiyatsbus - All Floors
Queen's Necklace (15/Empress) in Path of Kaitul - All Floors (weak to gun damage)
Stone of Scone (20/Fortune) in Path of Akzeriyyuth - All Floors (immune to physical, weak to curse)
Koh-i-Noor (25/Priestess) in Path of Adyeshach - All Floors
Orlov (30/Strength) in Path of Sheriruth - Floors 1-5
Emperor's Amulet (35/Hanged), Hope Diamond (40/Death) and Crystal Skull (50/Fool) can all be found in Path of Sheriruth - Floors 7-13 (Japanese Wiki says Amulet in 7/12/13, Diamond in 9/11-13, Skull in 7/11/13 but I also found them on different floors)