Note that in this video, I'm hugging my own right shin with my right hand, helping to trap my partner's right foot. This is worth playing with, as it helps to keep your partner from ripping their leg free. As you're making the transition to the back, be safe with your left foot, so you don't get caught in a toe-hold.

Quick Tip on Entering Into the Inversion: Lift your hips up, get the "leg underhook", and then, as you drop your hips, use gravity to help start the inversion movement.

If your partner allows you to sit up and grab their waist, you may be able to pull them into your lap, as mentioned previously. However, in no-gi, it's far more likely that they'll be trying to keep their hips away from you. In this case, pushing them forward is the way to go.