It is usually an INT check
According to the Player's Handbook, a DM might ask for an Intelligence check when a character needs their memory. See page 177, "Using Ability Scores", "Intelligence" (emphasis mine):
Intelligence measures mental acuity, accuracy of recall, and the ability to reason.
An Intelligence check comes into play when you need to draw on logic, education, memory, or deductive reasoning.
Player's don't roll for checks by themeselves
Can they roll a history check to see if they remember things from the previous session?
Your players should roll Intelligence (History) when an only you, the DM, ask them "make a History check". They can't just "roll a history check" by themselves and then, if the roll was good, ask you to give them information. See PH, page 174:
The DM calls for an ability check when a character or monster attempts an action (other than an attack) that has a chance of failure. When the outcome is uncertain, the dice determine the results.
Asking for a check is not an obligation. You can ask for a dice roll, or you can use your common sense and game knowledge to resolve the outcome. It is your job as a DM to find your own approach that works best in this particular situation. See DMG, page 236 "The Role of Dice":
Some DMs rely on die rolls for almost everything.
One approach is to use dice as rarely as possible.
Many DMs find that using a combination of the two approaches works best.
