The Aqua-Evac is for quick evacuation from the Ulysses, so it's not really designed to easily return to it. However it is possible, though a little tricky.

1. Position the Aqua Evac under the tail of the Ulysses, facing outwards
2. Fold the fins using the button on the bottom-right of the cockpit
3. Swim outside, and connect ropes from the rope anchors next to the hardpoint, to the small winches on the exit ramp of the Ulysses
4. Hit the retract button next to the small winches
5. Get back inside the Aqua-Evac, and use its controls to try and line it up with the hardpoint connector. Once connected, you will be automatically retracted inside the Ulysses

See attached photo for rope anchor locations
https://imgur.com/a/kxndfVy