TMZ exclusively obtained the video showing Liam briefly stepping out of an elevator in the basement of the CasaSur Palermo Hotel in Buenos Aires... chatting with one of the 3 people charged in connection with his death.

Our sources at the hotel tell us the staffer who shakes hands and chats with Liam in the video is Ezequiel David Pereyra ... a bellboy at the hotel who police say delivered drugs to Liam in a soap box. While police have not yet confirmed it's Pereyra in this video, we know they have the footage.

It shows Pereyra stacking chairs in the basement with other hotel staffers when the elevator door opens and Liam pops out, they share some words and slap hands ... and then Pereyra heads out through a doorway.

The video was recorded around 2:04 PM ... about 3 hours before Liam fell to his death from the balcony of his third-floor hotel suite.

Based on the interaction here, it appears Liam and Ezequiel are pretty friendly ... possibly because they knew each other already, and had met previously during Liam's stay in Buenos Aires.

As we reported ... prosecutors say Liam did not die by suicide, stating he plunged to his death as a result of the effects of the drugs he took.

Three people have been charged in the case -- Pereyra, a friend who allegedly abandoned Liam, and also an alleged drug dealer ... who has since spoken out and denied ever supplying Liam with drugs or receiving money from the late One Direction singer.

Cops say Liam had his drugs delivered in a Dove soap box ... and police say only hotel staffers had access to the resort's soap supply.

According to the autopsy, Liam had cocaine, crack, ketamine, ecstasy and a form of crystal meth in his system when he died.