Partially built ships during changes

When star is building, say 4/3 of ship per hour, I got it should produce 4 ships each 3 hours. It seems to me that if this construction speed is changed, the partially built ships are retained. So if it builds ships for 1 hour and makes 1 (with 1/3 partially built one hidden) and then the speed of construction gets changed to 5/3, there will be 2 new ships next hour (1 and 2/3 to finish the partially built one). Is it so?

If yes, are these partially built ships retained also during change of ownership? I mean, if other player makes 4/3 of ship somewhere and I capture that star one hour later, will I immediately get 2 new ships during that end of hour tick?

Um, yes, I think so.