Advanced Bind Lifters are for gear that is BOP (Bind on Pickup). Bind Lifters are for gear which is BOE (Bind on Equip).
As Arkana pointed out, using one ABL on a piece of BOP gear makes it permanently BOE going forward.
Most blue and green gear is BOE, all purple gear is BOP. Doesn't matter where it comes from- mems, EOJ, proofs, boss drops. Only exception to that rule is MOST crafted gear (the Dragon accessory sets comes to mind- they are purple crafted BOP).
Using an ABL on gear you intend to agg is crazy. Do what Bent suggested instead, and aggregate it to white cloth cheap unbound gear and trade that gear to whomever. They can then use another agg to get it into their wardrobe.
Since you are on Grimdal (I think) you can probably also PK trade bound gear. Just pk the other player til the item you want to trade drops. That still works, right?