Hi Jan, excellent choice.
I did similar one from Teryho chata to Zbojnicka chata and then to Chata pod Rysmi four years ago in 12h. You can expect snow at the highest parts of the route. It might be handy to have an ice axe (light one is enough). We have experienced all kind of weather on the trip. Snowing, sunshine, morning cold and wonderful sunset.
Good luck,
Peter

P.S. Note the good advice from @dinoboy

Hi Jan. U can use this online map mapy.hiking.sk/?ref=navigator… and by rightclicking "zacni trasu" + "pridaj medzibod trasy" + "ukonci trasu" u can calculate the time for your own route, because from Zbojnicka chata u have 2 options. Go through saddle Prielom, which takes less time (about 9hours) but is closed till 15.06.2018 and can be little bit dangerous, especially in bad weather conditions or go back to Hrebienok and follow the red mark (more then 10h walk). Maybe the best way is to ask staff on Zbojnicka chata about their recommendations regarding to actual weather conditions. Enjoy your trip.

max time is 4-6 hours / 15 km

we have been visiting slovakia for more than 20 years and have also made beautiful walks. We would like to have new routes. Routes in the low Tatras, high Tatras (and Mala Fatra)
look at slowakije-veenstra.nl$ret
E:janco.veenstra@ziggo.nl

Hi Jan, it depends on many factors - apart from your stamina and the weather, also for ex. the weight of your backpacks and shoes :) However, after this: outdoorfilmy.sk/…/ako-sa-mont…, the ascend to Chata pod rysmi is much more easier "technically", so most probably it may be the "breath" of your teammate with the worst stamina as the main determinant, if all the rest works out well for you. In good conditions, it is feasable to do it in 9-10 hours.

Hi Jan. Hikeplanner (application on hiking.sk) shows 9:35 hrs. My personal experience is generaly aroud 70% of hikeplanner time estimations (e.g. if hikeplanner estimates one hour walking it takes me around 45 minutes). But please be avare of the fact that the weather in High Tatras might be even in June wintry. You can face 25 degrees but you can also freeze and struggle with icy rocks, ladders and chains. In such case it can take much longer than any hikeplanner shows (Just FYI - until 15 June there is a seasonal closing of many paths in High Tatras)