。
Koizumi succeeded Mori as Prime Minister.
Literal
Koizumi-[formal-suffix-氏] [subject-が] prime-minister [as-として] Mori-[formal-suffix-氏] [attributive-の] after [object-を] succeeded-to.
Political news reporting. 後を襲う is a set phrase meaning 'to succeed (someone) in a position,' literally 'to attack the after' — an interesting case where 襲う, which normally means 'to attack,' carries the archaic sense of 'to inherit, to take on a mantle' in fixed expressions. ~として 'as' marks the role. 氏 is the formal journalistic honorific for named persons.