From the last meeting of the Master of Mankind and his Primarch-Son; Magnus, there was an offer of forgiveness, of redemption and of salvation. As documented by the scholar of this meeting, Magnus refused the offer and embraced daemonhood. Here the warp-entity alters that timeline, instead of refusing the offer, the Primarch embraces his Father and the Thousand Sons stand with the Imperium through the rest of the Horus Heresy. 

The Solar Brotherhood are above all else fiercely loyal and faithful to the Emperor and his vision for the Imperium. After being offered forgiveness for the Legions previous offences: the ignoring of the Edicts of Nikea, the arrival of Magnus into the Imperial Palace with a tide of daemons at his heels; these and all of the Legions sins were forgiven by the Emperor himself and the Sons of Magnus joined the Imperium once again in the fight against Chaos. The Solar Brotherhood are the name they chose to have henceforth; renouncing the Thousand Sons history and moving forwards with pride, their use of psychic abilities allowed, but regulated. Magnus and his sons then grew their Legion back to a size befitting an army of the Imperium, using new technologies and advanced armours and weapons; gifted from the Master of Mankind.