I travel with kegs to events. They'll shake up.
You definitely want to "jump" the clear, carbonated beer into a clean, pre-purged keg, leaving the sediment behind.
Liquid-out to liquid-in. And if you have one, a spunding valve on the receiving keg's gas post. If not, just gently release some extra pressure whenever the transfer starts slowing down.
As soon as you see milky beer appear in the transfer tube, pull the receiving keg's liquid QD off the post. Toward the end of the transfer I keep my hand on that QD, with the collar already lifted, ready to pull in a split second.