Run a mono signal from the Preamp output, into the 5153 FX return jack. Be aware the volume on the Pre will control volume, the controls on the 5153 will do nothing, and it will be as if the master volume is wide open.
That's not entirely true. The Presence and Resonance(?) will still function on your 5150III. The volume might as well, it depends if it's after the loop or not (and it probably is). But yes, Guitar -> Quad Preamp -> 5150 FX Return.