457(f) distribution - can it be deferred into a 457(b) plan?

[Pension Nerd]

I have a participant due to receive a distribution from their 457(f) plan in August. they also participate in a 457(b) plan.

The 457(b) plan does not exclude "distributions from an unfunded deferred compensation plan" from the definition of compensation.

If the participant makes a timely election (by the end of July), could they defer from the 457(f) distribution (which they will receive via payroll) into the 457(b) plan. Or should that compensation not be allowed to be deferred into the 457(b) plan?

If it's the latter, I would so appreciate a reg cite :-)