When followed by a participle, the common phrase after having is a redundancy. Both after and having indicate that the action about to be described has been completed, so using both is unnecessary. This redundancy occurs in all sorts of publications—for example:
But Niese left with one out in the fifth after having walked five. [NY Times]
After having lived abroad, Franqui moved to Puerto Rico in the early 1990s . . . [AP]
However, the government was careful to ensure ample funding for health after having spent much of the year wrangling with states over a new system . . . [The Australian]
There are two ways to fix this redundancy. One is to use only having:
But Niese left with one out in the fifth having walked five.
Having lived abroad, Franqui moved to Puerto Rico in the early 1990s . . .
However, the government was careful to ensure ample funding for health having spent much of the year wrangling with states over a new system . . .
Because, as in the first and third examples, this solution can create awkwardness, the better solution is usually to use after on its own and to change the tense of the participle from past to present:
But Niese left with one out in the fifth after walking five.
After living abroad, Franqui moved to Puerto Rico in the early 1990s . . .
However, the government was careful to ensure ample funding for health after spending much of the year wrangling with states over a new system . . .
