Was Abel regenerated before the offering according to the Calvinist? Genesis 4:4–5 [Berean Study Bible]
  (4) The LORD looked with favor on Abel and his offering
  (5) but He had no regard for Cain and his offering 


I'm in the middle of conversation with a Calvinist in a Christian Forum (in our language). 

First I ask that how come while both of them were totally depraved, but one of them (who is Abel) favored by God. After some back and forth respondings, to my surprise finally he said that it's because Abel is the elected one.

And he gave me Hebrew 11:4


  By faith Abel offered to God a more acceptable sacrifice than Cain's.
  Through this he received approval as righteous, God himself giving
  approval to his gifts; he died, but through his faith he still speaks. (NRSV)


He give the chronology like this :
1. God elect Abel before the foundation of the world. 
2. He regenerate Abel in time and give him faith, don't know when but before the offering event 
3. Those 2 points above causing Abel do a correct offering.
4. Now God has a reason to look with favor on Abel + his offering
5. and now God can give him approval as righteous through his offering.

When I asked him if he has any reference from any Reformed Church's father, he said he would ask his Church about it. But so far he hasn't followed up.

My question here is the same :
Is there any reference from any Reformed Church's father indicating that Abel was regenerated before the offering ?
Calvin addresses this in his commentary on Genesis 4, arguing that Abel was already accepted by God when he made this offering:


  We must, however, notice the order here observed by Moses; for he does not simply state that the worship which Abel had paid was pleasing to God, but he begins with the person of the offerer; by which he signifies, that God will regard no works with favor except those the doer of which is already previously accepted and approved by him.


A bit later, Calvin states the general principle, that everything done "before faith" is offensive to God:


  All works done before faith, whatever splendor of righteousness may appear in them, were nothing but mere sins, being defiled from their roots, and were offensive to the Lord, whom nothing can please without inward purity of heart


In Calvin's thought, faith and regeneration go hand in hand – in this section, he writes "faith is a gratuitous gift of God, and a special illumination of the Spirit" – so thus we see that Calvin believed that Abel was already regenerated and saved at the time of this offering.