want to replace my old 3 way light switch

I bought slide dimmer FEIT and want to replace my old stairs basement light switch, however I am not getting how the current wiring is done

I am attaching the current diagram ( I am bad in diagrams )

new switch ( slide dimmer) has 4 wires : 1 black 2 red and 1 green

I assume my current setup has not a ground ?

A1 and B2 are always hot
A3 and B1 are hot only when then light is on
A2 and B3 noting even light is on or off

so my question :

is the wiring should be like this

• A1 ( 2 black) to Black dimmer

• A2 ( white) to Red dimmer

• A3 (black) to Red dimmer

• B2 ( white ) to Black dimmer

• B1 ( red ) to Red dimmer

• B3 ( black) to Red dimmer

the green dimmer wire will be left unplugged

Thanks in advance