Torah Temimah cites Kerisos 27b.
One who designated his chatas and then died — his son may not bring it after him, as Scripture says “and he shall bring his offering” — he fulfills his obligation with his own offering and not with his father’s offering.
Diyuk of “korbano” — the offering must belong to the one who is obligated; the heir cannot discharge the father’s personal chatas.
A chatas that has been designated by a living person who subsequently dies cannot be brought by the son. The obligation is personal; it dies with the owner. The heir is not considered the continuation of the father’s obligation for purposes of this private chatas. The verse’s insistence on “his offering” excludes the use of an animal that belonged to someone else, even a father.