You can export, then import rules on a per stream basis but because the source and destination streams are changing some editing is required on the intermediate csv file. The export/import options are available from the Preferences page.
So for example:
The csv file format for Custom rules is (this type of record appears at the start of each rules section):
In the webui you would go to the current stream to be copied and Export the Custom rules to a csv file. Then you would use an editor to change all stream fields from the "current stream name" to the "new stream name". Then go to the new stream in the webui Import the file.