Is the purple wire on AC blower motor common wire?

I’m replacing my AC blower motor. The old one had Red,Blue, Black wires for speeds, white Common, and brown & brown/white wires to the capacitor. (Yellow, purple wires for rotation).

The new motor has one rotation direction.
It has brown and purple wires going to the capacitor. Black, blue red for speeds. Where is the common wire?

According to the photo I’ve attached, am I supposed to connect a second wire to the capacitor terminal with purple wire, and connect the other end of this second wire to the control board connection where the white wire previously was?

Like this?