Sending allows you to "contact a particular creature with which you are familiar". The question stipulates that caster was familiar with the creature in life, so the two questions we must answer are:
- is a petitioner a creature?
- if so, are they the same creature they were before becoming a petitioner (that is, are they still the "creature with which you are familiar")?
Is the petitioner a creature?
Becoming a petitioner is "just" acquiring a template:
“Petitioner” is an acquired template that can be added to any creature whose soul migrates to one of the Outer Planes following its death (henceforth referred to as the base creature). The petitioner uses all of the base creature’s statistics and abilities except as noted below.
Size and Type: The creature’s type changes to outsider. It loses all subtypes. Its size does not change.
Skills: Petitioners lose all skill ranks they possessed as mortals. As a 2 HD outsider, a petitioner has 12 skill ranks it can spend on skills (with a maximum of 2 ranks in any one skill), and gains bonus skill ranks as appropriate for its Intelligence. Unlike most outsiders, petitioners do not gain an additional 4 class skills beyond those available to all outsiders.
-- Bestiary 2 (also, PFSRD)
Nothing in the petitioner template would indicate that becoming a petitioner means that the creature is no longer a creature; if that were the case, the type change should include that, if nothing else. Further, the "skills" section reinforces the interpretation that a petitioner is still a creature: they must be, since they're a 2HD outsider that gets skill points based, partly, on their int.
So, a petitioner is still a creature. One hurdle down. But, are they the same creature?
Is the petitioner the same creature?
The Petitioner template says nothing about becoming a different creature - in fact, they: retain "fragments of [their] memories from life". Further:
Creatures who die, become petitioners, and then return to life retain no memories of the time they spent as petitioners in the afterlife. A petitioner who dies is gone forever...
The petitioner retains fragments of their memories, and they can return to life. If they were a different creature, there's no reason to believe that they'd retain any memories from life. Further: were they a different creature, there would be no sense in talking about their returning to life.
Additionally, petitioners "are the souls of mortals brought to the Outer Planes after death in order to experience their ultimate punishment, reward, or fate." If the petitioner is not the same creature that they were in life, there would be no sense in talking about their punishment, reward, or fate: a petitioner being rewarded or punished for what some other creature did in life would make no sense in the cosmic order.
Finally, the PathfinderWiki entry on souls states that:
At the end of the creature's mortal life, its soul leaves its body and manifests in the Ethereal Plane, beginning its journey with other souls via the River of Souls
The creature's soul - which, since the petitioner is now an outsider and, thus, no longer has a body/soul duality - journeys via the River of Souls. That is, the creature follows the River to wherever the cosmic order (overseen by Pharasma, of course) directs it.
So, yes: a petitioner is a creature and is the same creature that it was in life.
However, petitioners only retains fragments of its memories. A petitioner on the receiving end of a sending spell may not remember who the sender is, nor what the context of the message may be. Even if it does, it won't necessarily remember the answer to any particular question; getting information from a petitioner this way is not a guarantee by any stretch of the imagination.
Setting aside Petitioner's statistics for a moment, the answer can be found in the lore about what a Petitioner is (conveniently up on the Wiki). Specifically
Once a soul becomes a petitioner, it is irrecoverably altered. At this point, the soul's relationship with its mortal vessel fully ends—a petitioner gains a new physical body formed of quintessence and can never be resurrected into its previous mortal form.
The Petitioner is not the same creature as the soul that makes it.
I can see both sides of this and don’t have a specific actual ruling I can find but I’mma just lay out my thoughts on it.
In favor of it working I would say that since Petitioner is just a template added to a creature after death and as such it is the same base creature then yes, sending should work if you were familiar with it in life. Though whether the Petitioner is still familiar with them is up for debate as they hold on to only fractions of their memories from life.
Against it working would be that the spell Speak with Dead exists and I would say supersedes Sending in this particular purpose so you may not want to muddle up the effects of spells because if so then Sending just becomes inarguably superior to Speak with Dead except in the cases where you don’t know the deceased.
So all in all I guess my take is, depends on how liberal the DM wants to be to allow different spells to achieve similar results but I would be very stingy on what constitutes “being familiar with a creature” for the allowance of Sending in this way.