R – Exporting List Template from the CUstom List created using a Feature

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I have created a Custom List Template and wrote the Schema.xml,feature to deploy it,Installed to the server created a List based on that. Everything is fine. Now I wanted to Save this List as template and Deploy it to a different machine (Different SharePoint Server). But that feature is not visible in the Template List, when we try to create a New List. I have experienced it before. I wanted to know if someone else has come across this issue and is there a way to get it working without installing the feature again?

The Reason why I want to do this is that, SharePoint Administrator don't want to allow the custom List Template being deployed as Feature, he wants the things to be created as a STP file. We have created around 40+ Custom List Template and doing all the things manually to get the stp file is not an option. So I wanted to see is there any option so that I can save the existing list created using the Feature be saved as Template and reused.