I don’t think Web Reports has anything built-in to the interface for transferring the reports, but there are a few options.
If you are comfortable dealing with the SQL directly, there is a single column in the database that can be updated with the user ID number of the new owner. I won’t be back home until next week, but I can post a series of SQL statements next week.
If it’s only a small number of reports, another option is to use something like Chrome’s Developer Options (F12). View the report, press F12 to enter Developer Options, and in the Developer’s Console tab you can execute the WR.PrintReportXML() function. After a few seconds, the console should display the XML source of the web reports. You can copy the XML, and save that to a file with .besrpt extension. Then log on to Web Reports with the destination account, enter the “Report List” page, and click the “Import” button at the top to import the .besrpt as a new report.
If you’re ok with the report being temporarily public, you could also have the source account change the report to Public, log on with the destination account, view the report, and use the ‘Save As’ button to duplicate the report into the new account. Then the source account can log on again and change the report back to Private.