Marking laser position with glow in the dark material
The usual way to detect an IR beam is to use an "laser viewing card" or "IR sensor card". 

These are sheets of paper or plastic coated with a phosphor material that can be "charged" by multiple IR photons (I don't know if this works through a 2-photon process or by two charging steps through an intermediate state), and then emit a visible photon. They're sold by the major optical components distributors like ThorLabs, Newport, etc. The size of the sensor region is typically between 25 and 75 mm square. If you're working in an organization with some IR lasers already in use, look around and there should already be a few of these available.

I'm  not sure if these will maintain a glow for "a few seconds", but if you observe them with a sensitive camera in a dark room, they may work.