In Pegs and Jokers, is it legal to split a seven card between my peg and my partner's peg?
I think it depends on the variant that you're playing. This site lists the rules that come into play here. First, the basic rules:


  In the basic game, except in special circumstances described below, you may only move your own pegs.
  ...
  When playing a 7, you may either move one of your pegs forward 7 holes, or split the 7 between two of your pegs, moving them 1 and 6, 2 and 5 or 3 and 4 holes forwards. Of course the split move can only be made if you have at least two pegs in play.
  ...
  When, and only when, all five of your pegs are in the home (safe) position, occupying the five holes of your home track, you use your turn to move the pegs of your left-hand partner, if that player still has playable pegs. If left partner's pegs are also all home, you move the pegs of the next partner around the table who still has playable pegs.


As I read this, the ability to move your partner's pegs depends on the state of the game at the start of your turn. Player A still has pegs out, so he would not be able to split the 7 with his partner's peg; he only has one peg out, so he could not split the 7.

If you're using Arizona Rules, then it would be allowed:


  Throughout the game, you may move any of the pegs belonging to your team (so for example any of 20 pegs in the 8-player game with 4 on each team). Therefore you may discard without moving only if you are unable to play a card (other than a joker) that moves any of your team's pegs.


and this situation is explicitly mentioned in the North Carolina Rules:


  As in the basic game, you can only move your own pegs until your last peg is home. After that you move the pegs of the partner nearest to your left. You can use a split move to take your last peg home and move your left hand partner's peg with the remainder.


Because it's explicitly mentioned in the last variant, I do not think it is permitted in basic play.