We are so glad you reached out with your urgent prayer request. It's clear that you have a deep desire for unity and a shared faith in your relationship. Firstly, we want to commend you for praying in Jesus' name, as it is only through Him that we have access to God.
Let's focus on the key aspects of your request. You've asked for this individual to become a born-again Christian, which is a wonderful thing to pray for. We are reminded of the scripture:
"If you declare with your mouth, 'Jesus is Lord,' and believe in your heart that God raised him from the dead, you will be saved. For it is with your heart that you believe and are justified, and it is with your mouth that you profess your faith and are saved." (Romans 10:9-10 WEB)
We join you in praying that this person would sincerely confess Jesus as Lord and believe in His resurrection.
You've also prayed for total unity and agreement in your relationship. While unity is a beautiful goal, it's important to remember that true unity comes from both parties being deeply rooted in Christ. The Bible tells us:
"Make every effort to keep the unity of the Spirit through the bond of peace. There is one body and one Spirit, just as you were called to one hope when you were called; one Lord, one faith, one baptism; one God and Father of all, who is over all and through all and in all." (Ephesians 4:3-6 WEB)
However, we need to address that unity and agreement should not be forced or rushed, but rather a result of both parties growing in their relationship with Christ.
Regarding your prayer for a deeper relationship and increased desire for each other, it's crucial to approach this with biblical principles in mind. We should be cautious to avoid the appearance of evil by remaining pure in our thoughts and actions. The Bible tells us to:
"Flee from sexual immorality. Every other sin that a man can commit is outside the body, but he who commits sexual immorality sins against his own body." (1 Corinthians 6:18 WEB)
This warning is not just for physical actions, but also for our thoughts and desires. It is good to desire a deeper connection, but it must be done in a way that honors God and maintains purity.
Let's pray together:
"Heavenly Father, we come before You in Jesus' name, lifting up this beloved sister and the individual she has brought before us. Lord, we pray that You would work in his heart, drawing him to Yourself, and that he would confess Jesus as Lord and believe in Your resurrection. We pray for unity, Lord, a unity that comes from both of them being deeply rooted in You. Help them to grow together in faith, and to desire a deeper connection that honors You. Keep them pure in thought and deed, and guide their relationship according to Your will. In Jesus' name, we pray. Amen."
Prayer Focus: God, Thank You for loving me. God, I ask You in Jesus’ name please bless me with everything that I stand in need of and everything You want me to have. 
