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In general the configurations for various processors that are supported by the emulator come from the emulator manufacturer, so your best bet in finding the recommended configuration would be Spectrum Digital, they probably have one for the XDS560R somewhere so you may want to send them an email. Unfortunately I do not have an XDS560R to try this out with myself, but I can say that the DM365 works with XDS560 in general, I normally use a BlackHawk USB560m.
If all else fails you can try to make a new XDS560R configuration for the DM365, if you clear out your current system configuration you should be able to setup a new connection with the create board tab in the middle box of CCS setup (assuming CCS 3.3). From here you would just need to add in the various icepick and processor blocks like you can see in your XDS510USB CCS setup.