Global Mapper v25.0

LiDAR Import, Colour, Export - Re-projection Required?

Sulphur
Sulphur Global Mapper User
edited May 2015 in Projection Questions
Here is what I'd like to do:
- Load a Map Catalog (of satellite imagery)
- Load a LAZ file
- Apply the colour to the point cloud
- Export a LAZ file (in exactly the same position as the input file)

I understand that the input LAZ has to have a projection, otherwise it won't line up with the imagery.

I want the output file to be exactly the same as the input file, with the obvious exception of added colour (and therefore possibly different point size and version).
The LAS header offsets, the points X, Y, and Z - all the same as the input file.

How would I go about this?
Would I need to create a projection to "get it back" to where the input file is positioned?
Is my understanding of projection not quite correct?
What tutorial videos should I watch?

Thanks for any help