In a mixing bowl put together the apple puree, egg white and 150 grams of white sugar and beat all together until there are stiff peaks and the mass become double or triple in size (it will take approximately 15 minutes).
In a metal pot put together 300 grams of white sugar, agar powder and the water. Warm the mass up using medium heat (it will take 10-15 minutes). When the mass starts to boil continue to warm it up until there is a thick and a little bit yellowish sugar syrup. It is ready at the moment when the temperature in the pot reaches 110 degrees C.
Start to beat your egg-puree mass again and at the same time slowly add the hot sugar syrup. Mix it all together until you have very shiny and a stiff mass again (it will take 10-15 minutes).
Fill your zephyr mass in a piping bag and press it out from the bag on the baking sheet. You can make a small circle to get the rose shape.
Let your zephyrs to dry at room temperature. You will need to wait from a few hours (in a hot and dry summer) until up to 6 days (in a cold and rainy autumn) till you will be able to eat them.
