Who sends Pops back in time in Terminator Genisys?

As was mentioned in the other answers, the movie never answered this question. However, we have this official answer from io9:

Who sent the Terminator back to 1973 to protect a young Sarah Connor?

This question is purposely left unanswered in the film, but would potentially be answered in a sequel, if that happens. However, writers Laeta Kalogridis and Patrick Lussier did confirm they know the answer.

But as we now know, the Terminator Genisys sequel has been cancelled and the future sequel is going to be a direct sequel of Terminator 2: Judgment Day.

So, really, only the writers know, and we won't know until they tell us.

This was also covered in a similar post from our sister site, Science Fiction & Fantasy.

It's not actually answered in the movie - several theories have been given such as Jacobs answer but there is no official explanation. Most likely this information will be brought up again in a later movie.

Pops (Arnold) did what Sarah Connor said and in the credits Genisys survived the blast. This means that there could still be terminators in the future and Sarah Connors can reprogram a T-800, erased its memory, and sent it back to save her in the early 70's.

Right, so listen carefully as this is tricky to keep track of.

We have 3 terminators sent back and 1 Kyle Reese:

• T800 Arnie - sent to 1984 (as is Kyle), and this happens in both T1 and Genisys
• Good Arnie - reprogrammed by (a) John Conner in the future
• T1000 prototype - sent to same time as good T800.

So in T2, good T800 goes to when John is a youth and Sarah is a mature adult. What we can surmise is that the events in T2 (I'm going with Cameron et al and T3/salvation didn't happen) changed the timeline (as T1 changed things for T2).

So given also that Sarah journeys to 2017 from 1984 (so missing the T2 timeframe), and we don't see John Conner at this time it's fair to assume that in this alternate timeline the good T800 and T1000 were instead sent to 1974(?) when Sarah is young.

From this, we can see that Pops and T2 T800 are the same, and the T1000s in T2 and Genisys are the same (why the different face, not sure, but Lee Byung-hun is both an established actor and has established martial arts skills so maybe something for the next installment?)

So by this thinking, Pops was sent by John to protect Sarah, but by some method, we don't know as there wasn't a time when Kyle goes back and sees the attack on John.