The fruit has about the size of a medium-sized apple. The small tree grew in the botanical garden of Funchal, Madeira, but unfortunately had no label. The seed had already germinated inside the fruit.
Thank you, I also had thought of something like this. But I am quite sure it isn't Eriobotrya. The fuit was quite hard (pumpkin-like - also inside), without hairs and much larger than loquat. Also the leaves were different and glabrous.
I don't know who or what has added the term "Sapotaceae" to the question topics below my pictures (together with "Botany", "Plant Taxonomy" etc.), but searching within this family I found that it is obviously Pouteria (P. obovata, Lucuma). I am astonished.... Still: thanks everyone...