The children of thy elect sister greet thee. Amen.
The verse is the closing greeting of the letter, conveying greetings from the children of the elect sister. The letter itself is addressed to a Christian woman, the elect lady, and her children. That woman is understood to represent the church, and is a church.
She and her children are not an individual woman and her family. The elect lady and her children addressed at the opening are therefore a church, and the children of the elect sister who send greeting at the close are another church. The greeting thus passes from one church to another church.
The verse is the closing greeting of the letter, conveying greetings from the children of the elect sister. The letter itself is addressed to a Christian woman, the elect lady, and her children. That woman is understood to represent the church, and is a church.
She and her children are not an individual woman and her family. The elect lady and her children addressed at the opening are therefore a church, and the children of the elect sister who send greeting at the close are another church. The greeting thus passes from one church to another church.