This issue can be complex as it involves Windows SID (Security Identifier), which is not supposed to be changed or duplicated on another system. Here's few suggestions that may help you:
Method 1: Modify Program Settings Manually
If these settings are manageable and not too complex, you can manually adjust the settings of this program on the new computer. This approach is more secure and should work effectively, provided you know the configurations from the old system.
Method 2: Use Migration Tools
You could use tools specifically designed for this purpose such as User State Migration Tool (USMT) provided by Microsoft. These kinds of tools are developed to synthesize user's state from one computer and then transform it in...