SYMPTOM:
After adding extended property sets in the Extended Property Editor for a project, a user might need to move those new extended property sets to another project in a different environment, as shown below:

However, it is currently not possible to move those new extended property sets by Strategy Object Manager 10.x.
NOTE: If there is a same name property set in the destination project already, the property set value can be moved by Strategy Object Manager 10.x.
CAUSE:
Strategy Object Manager 10.x is not designed to resolve the conflict in case there is another similar or same extended property sets already existing in the destination project.