InfoPath Dev

Working in SharePoint 2016 on prem. If I have a list with a customized InfoPath template, is there a way to copy that customized template to another list? I created my "child" lists from a template of the parent list, but now I'm noticing that only the parent list has a customized template - so I'm wondering if I stupidly customized it AFTER creating all of the child lists based on it...The child lists need to have functionality where, when the user clicks on a checkbox it'll add notes into a multi-line text field (recording a history of certain interactions they need to take with the form) so it's not functionality I believe I can create using the OOTB list column settings.
Now that I know that the parent list is customized properly, I could re-save it as a template and recreate the child lists from that but there are a LOT of them so this is my last resort...And frankly I'm not 100% sure the customized template would carry over anyway...?

I think if you save a list with a customized form as a template, that form will also be applied to any lists created from the template .... but that should be pretty quick to test. Unfortunately, I don't know of a way to publish a form to another list. There may be a way to do this in the source files - here's one blog post I found when searching on this topic: https://www.c5insight.com/Resources/Blog/tabid/148/entryid/613/how-to-migrate-a-sharepoint-2010-infopath-list-form-to-sharepoint-2013-or-sharepoint-online.aspx