Tried loading my Creative Suite software to my MacBook Air and says issue with serial numbers. 1 user, 2 computers...can you do that?
You should not be trying to transfer from one machine to another if that is what you are doing (your posting title makes it sound that way). Use installation files and make sure the serial numbers agree with what your Adobe account lists for it.
A single user license allows you to have two activated installations. As long as the two machines meet the system requirements for the software you should be able to install and activate on both.