How can I motivate an employee who is leaving to share their knowledge with their replacement?

That would depend on why they are leaving & how they were treated while they worked there. If they got along & were treated well by their employer, manager & coworkers they are usually pretty open to helping train their replacement.

Pay them double time to do it.

A good employee will support training his replacement - my creed is that "a person is not just what he is actual doing. a person value is what he or she leaves behind" ..you need to pass the knowledge, lesson learned to the next person.

Pay the leaving employee for their time training the replacement. If the employee is being fired and is bitter about it, pay severance. If they are leaving on their own, talk to them about taking some time to do the training for overtime pay. Basically, motivate them by paying them.

Offer training pay

Make it their only job. Make it easy for them... record meeting sessions rather than have them try and write down everything. Get good questions from the replacement person for the departing person.

There’s no way unless the person leaving is leaving on good terms which most likely ain’t the case