Move License to Another Laptop

Directory Opus -
Per the licenses I purchased, I can install on 2 computers + 1 laptop (so 3 installs). The laptop I installed on has failed and I uninstalled Directory Opus. I now want to install Directory Opus on the replacement laptop (This would represent the 4th installation under the same license).

Q1: Did the uninstall de-register the license?

Q2: When I try to install again on the new laptop, will it install correctly? (this would represent the 4th installation on the same license).

Thank you.

There's nothing special you need to do, just install on the new laptop and away you go.