I have tried Points to line, the result is a line that matches the original line I have, with an attribute table with only objectID, shape and shape length.
Snapping points to line I cannot use unfortunately as I only have the Basic license.
I have tried Spatial join (join one to many), but with around 400 points for each of the two lines this just results in a line with attribute table consisting of around 400 20km rows with different z values.
Thank you for your time, Dan.