In John 7:3-5 (NASB)
3 So His brothers said to Him, “Move on from here and go into Judea, so that Your disciples also may see Your works which You are doing. 4 For no one does anything in secret when he himself is striving to be known publicly. If You are doing these things, show Yourself to the world.” 5 For not even His brothers believed in Him.
In Acts 1:14 (NASB)
14 All these were continually devoting themselves with one mind to prayer, along with the women, and Mary the mother of Jesus, and with His brothers.
From John 7 to Acts 1 we see there's a conversion of James, the brother of Jesus.
The question is in regards to 1 Corinthians 15:7 (NASB)
7 then He appeared to James, then to all the apostles;
was James converted before or after resurected Jesus appeared to him?