When a template is created on a certain API key, it can be directly used only when sending messages using that API key.
However, it is possible for a template created on a primary API key (and its contents) to be visible for all sub-accounts. To do that, when creating the template on the primary account, set its OwnerType property to user.
The contents of templates with the user owner type can be retrieved by a sub-account using GET /template/{template_ID}/detailcontent. Then the sub-account user can simply copy the content and insert it into a template created on the respective sub-account API key using POST /template/{template_ID}/detailcontent.