Hi @G4als
I definitely understand your concern in this situation, especially considering the investment made into your current store theme. I want to clarify some of the information already shared here for you so that you can get this resolved as quickly and seamlessly as possible.
First step is to find out what theme file you are using. Did the DMCA notice specify by chance? If not, and if you still have access to your store admin please go to Online Store > Theme > Edit Theme and click the 3 dots in upper left corner of the theme editor to view your theme details.
The top portion should show the theme file name, developer and file version. The View Documentation link or Get Support link should link you to the theme developer directly. If you can share that information with us here we can help you find your theme file and connect with the developer to finalize a license purchase, either by yourself or the developers you previously used.
A legitimate theme file purchase for a theme from the Shopify Theme Store will include a billing invoice in your admin for the purchase of the theme file. This is the proof of purchase and ensures you have a licensed theme file for your store. If the theme was purchased from outside the theme store then a proof of purchase that shows payment for this theme for your store from the developers directly is required.
Unfortunately, some bad actors copy and reuse the theme code across multiple stores. This goes against the license and terms of agreement of the theme file usage. Each license is good for one store only and if duplicated without a license and used on another store, that store can be subject to a DMCA notice from the developers.
The simplest method of resolving this will be to confirm what theme file you are using and purchase a licensed copy from the theme store. Once you have a license attached to your merchant account you can continue using the customized theme file you have. You do not need to switch out the theme file or transfer your changes, so long as the license is purchased for a version of that theme.
From there you can have the time you need to contact your original developer for payment of the theme license or take appropriate actions with them about this.
Alternatively, you can publish a different theme file on your store until you can resolve the issue of the theme license with your previous developer.