- In random danger - I'm locking on you, give me a few more seconds!
- On the far side of the "0" station (it's like a 4 minute sprint back)
- Near 0hp at enemy's ship/oxygenless planet/being munched on by antlions
- After bravely ejecting the enemy's reactor core
As an offset (and anti-spam/abuse prevention system) I'd propose the locking time to be inversely proportional to the square of velocity of the target when looked through the frame of reference of the teleporter (i.e. if both ships are moving at the same speed in the same direction so there is no apparent movement then only the walking/running/flying influences the time negatively).
If this would be getting implemented, the Devs could also decide if getting more than one person at a time would be possible - and how, sequential (one lock at a time, with a possible queue) or simultaneous (four clicks, four "locking on target" bars going simultaneously for the cost of power usage increased accordingly).
Optionally, the devs could make it possible, as an added incentive to boarding to force-teleport enemies onto your ship once you capture their teleporter (being on their ship makes it tuned to their quantum shields' frequency).
I think this suggestion would be a nice addition whether the teleport-on-warpjump system gets removed or not.