I doubt that the DR770 and 880 share a common sysex profile, so you're probably going to have to do it manually. Set the 880 for external clock, arm a pattern to record, make sure the MIDI OUT of the 770 is hookup to the MIDI in of the 880, and hit play on the 770.
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I am the stone that the builder refused...
What i would do, rather then juggle recording from unit to unit, is hook the Midi Out of your DR-770 to the Midi In of your DAW/computer sequencer.
Then simply hit record (is the DR-770 set to midi channel 10 like most drum machines?) on your sequencer... you can hit play on the drum machine, let each pattern play for a few bars to make sure it tracks well then change to others.
Save this midi template of sorts and then record into your DR-880. Now youve dont the transfer AND have a backup on file.