It doesn't have to be there, BUT you'd have to say "Pamatuji SI jeho slova." You get to choose either PAMATOVAT NA or PAMATOVAT SI (both followed by the accusative case). There is a slight difference but nothing you'd have worry about before you reach like C1. :D I'd say that the second variant is more common (but than again, this whole sentence sounds kind of bookish, so PAMATOVAT NA fits a bit better the style).

Jeho in this sentence is a possessive pronoun, not a personal pronoun. It is "his" here, rather than "him." Those little "n" changes happen with the personal pronouns.