We do not have the ability to move content from test to the live environment unfortunately. The test environment is meant to be used for testing proof of concepts or replicating issues that are reported on the production environment, not for extensive course building. There are tools on the production environment that help build courses that are hidden from your learners, such as the published setting and hiding from the course catalog.
Another thing to keep in mind about the test environment is that our testing team occasionally loads a copy of the production site to the test site. So if we are not aware of your testing on the site, your changes risk getting overwritten. Please let us know so we can check when that has been setup.
For the activity that you have set up in Test, the only option we have is to copy and paste between two browsers set up side by side. If you need further tips about moving it, let me know.