This is a long day hikeing to go up and back from Osnabrücker H.
Follow the marked way from Osnabrücker Hütte to the Ochsenboden. After about 0.5km from the house: the path cross the stream on a little bridge. Go up to the base of moraine from here and the track go up the ridge of the moraine (on about 2300m you could see the other side of the morain, what made the glacier before hundreds of years - it is beautiful-). After 50 meters that the path start to go away from the morein-ridge, turn left and go up hardly 120m levels. From here about 1.5km you can see Preimlscharte (from here the route hasn't so hard levels, but somethimes there are 20° steeply dipping panels). Before the Preimlscharte you have to cross Grosselendkees glacier. Walking up in the Preimlscharte is a little hard in summer because there is a little morein (like a conveyer belt). I think this is the most exciting part of the route. When you reach the top of the Preimlscharte turn a little right and go up to the ridge of Hochalmspitze.
You could see the two moraines on the centre of the picture