If a firstborn boy, for whatever reason, was not given a Pidyon Haben as a child, and he has already grown up and become an adult, who performs his Pidyon Haben? On the one hand, we might say that now that he has grown up, he bears personal responsibility toward this Misva, and he must therefore perform his own Pidyon Haben. On the other hand, however, one could perhaps argue that since the Torah imposed this obligation on the father, it remains the father’s Misva even after the child grows up.
This issue is subject to a debate among the Rishonim (Medieval Halachic scholars). The Ribash (Rabbi Yishak Ben Sheshet of Algiers, 1326-1408), in one of his responsa (131), cites the Rambam’s ruling that when a father performs the Pidyon Haben for his son, he recites the Beracha of "Al Pidyon Ha’ben," whereas if the son performs the Pidyon for himself, he recites the Beracha of "Lifdot." According to the Ribash, this ruling reflects the fact that once a firstborn boy grows and becomes an adult, he bears the obligation of Pidyon Ha’ben. This is also the ruling of the Mahari Kaspi.
By contrast, the Sefer Ha’hinuch (anonymous work from the period of the Rishonim), in Misva 392, writes explicitly, "The father is always obligated to redeem his son, even after he [the son] grows up." This is also the ruling of the Rashba (Rabbi Shlomo Ben Aderet of Barcelona, 1235-1310), who writes in one of his responsa (2:321) that the father clearly bears the Misva of Pidyon Haben even after the son reaches adulthood. According to this view, it is only if the father dies, Heaven forbid, or if, for whatever reason, he refuses to perform the Misva, that the son performs his own Pidyon.
As for the final Halacha, Hacham Ovadia Yosef rules (Yalkut Yosef – Soba Semahot, p. 247) that the father takes precedence regarding the Misva the Pidyon Haben even after the boy has grown up, and he recites the Beracha of "Al Pidyon Haben," as well as "Shehehiyanu." This ruling also appears in Yabia Omer (vol. 7, Yoreh De’a 28, p. 270).
In a case where a grownup firstborn must perform his own Pidyon Haben, he recites the Beracha of "Shehehiyanu" (in addition to the Beracha over the Misva). Although the Abudarham (Rabbi David Abudarham, Spain, early 14th century) maintained that a firstborn who performs his own Pidyon Haben does not recite the Beracha of "Shehehiyanu," the majority of authorities disputed this view, and maintained that "Shehehiyanu" is recited even in such a case.
Summary: If a firstborn did not receive a Pidyon Haben as a child, the father bears the obligation to perform the Pidyon Haben even after the child has grown up. If the father is no longer alive or does not wish to perform the Misva, then the firstborn must perform the Misva himself. The Beracha of "Shehehiyanu" is recited at the Pidyon Haben even in such a case, when a firstborn performs the Misva himself.