Agreed. "He prefers to take his retirement" is the literal translation and is good (if a little stiff) English, so should be accepted. If it isn't, report it.
Meaning is slightly different I'd say
He prefers to retire = He is not retired yet
He prefers retirement = You could argue that he prefers that above working, hence he's already retired.
I don't agree with this distinction.
However, there is a different distinction: "to retire" emphasizes the action of retiring whereas "retirement" emphasizes the state of having retired.
Thus, "He prefers retirement" says more about his state of being: he enjoys the gardening he missed out on while working, etc. Whereas "He prefers to retire" means it's the action that matters: "He was given a choice of being fired, which carries some shame, or of retiring, which also provides benefits. He prefers to retire."
Put differently, think about what would happen if you added "over" at the end. "He prefers retirement over ...", eg, "He prefers retirement over working", vs "He prefers to retire over ...", eg, "He prefers to retire over being fired".
I get your point but what we're doing is translating this sentence as closely as possible. Here we have an infinitive following the verb, so it would be a simple and direct translation of "He prefers to take his retirement." I would suspect that Duo would accept that answer; if not, it should. Duo likes "He prefers to retire" which is a reasonable approximation.
He would rather = he prefers. Il préfère prendre sa retraite = he would rather retire.
In addition, this is the most usual way to express this kind of meaning in English (also: He'd rather retire).
Is "prendre sa retraite" more;
An approximation of the verb "to retire" or;
The state of being in "retirement."
"Does your father want to do that three month construction contract?" - "No he prefers retirement/He would prefer to stay in retirement."
It is closer to "to retire", literally "to take his retirement" (to retire) or "to take his pension" (U.K.). The idea is that he is still working but perhaps he will leave his employment in order "to take his retirement". Using "prendre sa retraite" would indicate that he is not already retired. That would be "Il est en retraite" = He is retired.
I just wonder could this sentence be translated as He prefers to take his pension
"He prefers to take retirement"... whose retirement would he take other than his own?.
He prefers to go into retirement? That to me sounds more natural in English, but I'm not NS
No, it can only mean retiring as in to take your pension.