"The last office performed by her emaciated, trembling hand, was to trace a few lines to her parents. And did not God regard her last wishes and prayers for her parents? In less than two years, Father and Mother White were keeping the Bible Sabbath, happily situated within less than one hundred feet from our door. LS 156.2"
"Confess your faults one to another, and pray one for another, that ye may be healed. The effectual fervent prayer of a righteous man availeth much."
The EGW passage describes the fulfillment of a dying person's prayers for her parents. James 5:16 speaks to the power of prayer, especially the prayer of a righteous person. The connection is that prayer is effective.
"resurrection. We laid her beside dear Nathaniel in Mount Hope Cemetery. LS 156.3"
"For the Lord himself shall descend from heaven with a shout, with the voice of the archangel, and with the trump of God: and the dead in Christ shall rise first:"
The EGW passage mentions laying someone to rest in anticipation of the resurrection. 1 Thessalonians 4:16 speaks directly about the resurrection of the dead in Christ. The connection is the hope of resurrection after death.