Well, I've tried the method above, but it did not work for me (for some reasons). So, I tried multiple ways, including using timer and other tools.
Finally, I found an easier way to do the trick (maybe anybody will find it useful).
So, I make a box and set Platform and Solid behavior to them. I set Solid behavior initial state as "disabled".
Then, I create an event which concludes of two conditions. First: Player box is overlapping box at offset (0, 10). Second: Player box Y coordinate is less than box's Y coordinate. Then, assign an action: set Solid behavior enabled for box. Add sub-event: Else, box's Solid behavior is disabled.
This way lets you move boxes (I guess that precision can be achieved with tinkering with the Platform behavior of box) and it does not interrupt the walking animation of a player.