How do I copy Repository Connections info from one laptop to another ?
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Yes, you can zip the Eclipse workspace or copy it otherwise to a different machine and you can then open the workspace on the new computer and will have all metadata you want. I have done this a couple of times already.
Eclipse only stores this data in the workspace metadata. You can, but don't have to copy the Eclipse client. I would suggest to rather install a fresh version on the new machine and use the new Eclipse client with the copied Eclipse workspace.
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RTC has an export capability: File -> Export -> System Definitions -> System Definition IDs and it allows me to pick from a list of Repository Connections and to select various attributes to export... but when I do an import on the new laptop, the process first makes pick from a list of Repository Connections to import to... but my list of connections is empty so I cannot proceed with the import.