I am not quite clear on how you had created the initial form, did you create it as a tab from within a Channel in Microsoft Teams OR did you create it from Microsoft Forms in your web browser?
If it's from within a Channel in teams, the templated Form will be in https://forms.office.com/ and under Group forms and the SharePoint/Teams site that the form was created in:
You can go into the form, click onto Share and then onto + Get a link to duplicate. This will then give you a share link to give to others to then create their own copy of the form (without changing your template) and to then modify it for themselves.
If it's been created from your account via the web browser, you could just open the form and follow the Share steps above to give your colleagues access to using your template.