Time of day between morning and noon
Solution 1:
There is indeed no word for it other than 'late morning' or similar. Also, 'lunchtime' would be more idiomatic than 'noon' for the period round midday (or, I suppose, 'dinnertime' for those who always call their midday meal 'dinner', but that's another story).
I don't speak German, but your sentence would have to be translated as something like:
Maria had been up early, but Peter didn't get up till late.
Solution 2:
In everyday speech the time of the day you are referring to is called:
midmorning or (mid-morning):
the middle of the morning; the time centering around the midpoint between early morning and noon.
(Collins)
A few usage examples:
From washingtonpost.com
For most people, mid-morning is one of the busiest parts of the workday.
From huffpost.com:
Low-Calorie Mid-Morning Snacks To Eat Before Lunch
From food.ndtv.com
Mid-Morning Work Breaks Improve Health and Productivity
Solution 3:
I think it's futile to try to find a one-to-one translation from German to English. Just because German has Vormittag doesn't mean English should have an exact counterpart, which I don't think it does.
None of the English expressions such as mid-morning, forenoon, late morning is an exact counterpart of Vormittag.
In fact, Wiktionary defines it as all of the three:
Vormittag
- mid-morning, late morning, forenoon (time of day roughly between 9 a.m. and noon)
I think late morning is the closest but it can be entirely subjective depending on who you're asking when late morning starts.