Important note: If the Theme being used originated from the Shopify Theme Store, then a valid purchase of that Theme is also required on each account for a valid license, in order to use that Theme.
As such, the destination store will also need to purchase a valid license for that Theme as well.
Without a valid license, merchants are not able to receive support for the Theme from the respective Theme developer.
For your Theme, Replay is able to copy its coding and asset levels. If Images were uploaded (to your Theme or elsewhere) via the Files section of your store - as found via the Document/Files Uploader located within your Store Settings - Replay will be unable to access and copy those. Shopify does not yet allow access to this Files section.
We're working with Shopify on this and hope to eventually be able to copy this data in the future, but for the time being, any attachments and/or Images uploaded via the Files section of your store will need to be manually re-uploaded within your destination store.
For a complete breakdown of everything Replay currently can and cannot copy for you, please refer to this help article.