Zoom template ownership - change from Site to Account.

In Zoom Phone, I wanted to copy the Auto Receptionist settings to a template.  So I used the three dots menu (...) and found the Save to Template option.  When I went to apply that to another Auto Receptionist in another Site, I couldn't find it.  After some investigation, I noticed that the Owner of that template was in a different site.  Ideally, I'd like the owner to be Account.  Is there any way to change that?