I think schools should feel some kind of responsibility for their students after they graduate.
「卒業後の人生」は英語で次のように言えますが、文章で使うなら、下の例文のように言うと自然でしょう。
ーlife after graduation
ーpost-graduation life
例:
I think schools should feel some kind of responsibility for their students after they graduate.
「学校は生徒の卒業後も何らかの責任を感じるべきだと思う」
ご参考まで!