Grappling and reach/reach weapons

One of my players is a large creature with a 10 ft reach who is also using a lucerne hammer (10ft reach).

He mentioned grappling with it and I was hoping for verification.

How would grappling with a reach weapon on a reach character work?

Would he have to drop the weapon, is he unable to initiate grapples at adjacent squares?

Edit: I wanted to clarify, it isn’t that he wishes to pull an enemy to him, I k ow during a grapple you move into your opponents square.

My concern is whether or not he can initiate a grapple while holding a reach weapon and being a large creature as well as what ranges he would be able to do so at and whether he can do so while still holding it or does he have to drop the weapon.

For reference: reach weapons state you cannot attack someone adjacent to you while using it.

Initiating a grapple is considered a melee attack action that deals no damage.

The players has a feat called shortened grip that allows the adjacent attacks with reach weapons.