Skip, ignore or miss false value

[robg76]

I am looking to copy data from one cell to another, only if something is true. If it is false I want it to ignore the false side of things and not leave a blank cell, or put a zero or false. Just to leave the cell as is (as the cell will have data in already that I don't want overwritten.

Please see the attached file.
If any false HAS to be written, could it then write the false output to the blank cell to the right of it?

(Apologies if this has been answered before, I've searched and searched and couldn't find just what I was after, or adjust previous similar results to work for this scenario)