The player character can go prone in one fluid motion while moving forward (W, W+A, W+D), but unfortunately there are inconsistencies depending on stance (crouch - stand), weapon state (raised - lowered) and movement speed (walk - combat pace - run) due to this neat prone-on-the-move transition being missing in different occasions.

Below is a summary of my findings on the lacking transition.
Depending on the view (1st or 3rd person), some occurrences of the issue are more striking than others.

Pressing Z while moving forward (W, W+A, W+D) in:

1)CROUCH

  A)with Raised weapon
 
    Walk (missing! + character stop for a brief moment) *
    Combat pace (ok)
    Run (ok)


  B)with Lowered weapon

    Walk (missing! + character attempts to run for a moment)
    Combat pace (missing! + superfast stance change) *
    Run (missing!)

2)STAND

  A)with Raised weapon

    Walk (missing!)
    Combat pace (missing! + character stop in crouch for a brief moment) *
    Run (ok)


  B)with Lowered weapon

    Walk (missing!)
    Combat pace (missing!)
    Run (ok)