Jemandes Entwicklung is grammatically correct, however it sounds pretty ghastly.
I think there are two possible ways to translate your first sentence comfortably, but I would half avoid a direct translation.
I mean this in the sense that you say in English “it is a necessary stage”, then you use one’s, but actually we haven’t really intrduced exactly who this one is. In English it is clearly a passive construction, however in German there isn’t a nice way of expressing one’s — referring back to a person we haven’t yet introduced. Furthermore, there is no genitive form of man (English one), it only exists in the nominative, with possessive form (sein) and reflexive (sich).
I would rephrase the German to use man — in place of the English clause: it is a necessary …
After doing this, we can refer back to our man (the indefinite pronoun) using sein or the reflexive sich:
- Zum Zwecke seiner Entwicklung muss man diese notwendige Phase überwinden.
- Man muss diese notwendige Phase überwinden, um sich zu entwickeln.
A more direct way might be the following.
bei der Entwicklung eines Menschen ist es eine notwendige Phase/Stufe.
As a final note, I’d like to point out that these constructions are very uncommon i.e. using the genitive of personal pronouns. The most common way by far to express possession is to postposition von plus the person’s name. There may also (in South Germany) be the definite article thrown in for good measure. E.g:
Hier ist die Handtasche von (der) Maria
Other variants one might hear (Weitere Varianten, die man vielleicht hört):
Hier ist Marias Handtasche [Maria in genitive]
Hier ist die Handtasche der Maria [Maria again in genitive, shown by the article]
Another alternative to my first sentence would be die Entwicklung desjenigen
I listed them in descending order of usage (in my own experience!)
