Russell Brand To Pay for Smashed Window

The man who was INSIDE the office during Brand's alleged outburst in New Orleans Monday night tells us ... people connected to the actor reached out to him shortly after Brand allegedly grabbed the phone from a paparazzo and threw it at the building.

We're told Brand's people acknowledged Russell threw the phone ... and said Brand would cover the costs to replace the shattered window.

As for the iPhone ... the man tells us he returned it to the photog after cops got involved.