We/I are/am deeply saddened by the news of (Name of deceased) passing. Our/My thoughts and prayers are with you and your family. (Name of deceased) soul is now at peace. May my condolences bring you comfort, and may my prayers ease the pain of this loss.
“Rest easy” and “rest in peace” essentially mean the same thing. They both refer to death as a state of “rest” and reflect hopes that the person is enjoying a relaxed, peaceful state. If you're looking for a synonym for “rest in peace,” “rest easy” is a good option to consider.
Check in on them. Make an effort to check in with your friend, even if it is a quick phone call, a card or an invitation to grab a coffee together. ...
A simple “thank you” works. Other short phrases you can say are, “I appreciate it,” or “That's very kind.” If the other person knew the deceased and is grieving too, you can acknowledge that by also responding, “This must be hard for you, too.”
Both indicate comfort. If someone is focused on what you're saying, it's very common to see them leaning forward, resting their elbow on a table and their head in their hand.
In this early use, rest in peace (as requiescat in pace) was a prayer or wish that the soul of the deceased would find eternal peace in Heaven. Catholic burial services in particular still incorporate the original Latin requiescat in pace in this way.
My sincerest condolences for you at this time. You have my deepest sympathy and unwavering support. Wishing you peace, comfort, courage, and lots of love at this time of sorrow. My heart goes out to you at this difficult time.
A common belief that is shared is that the spirit of the deceased journeys towards heaven (or similar) after they have passed away. Saying “godspeed” during a funeral just shows people wishing the spirit of the deceased a safe journey to the afterlife.
Eternal rest grant unto him/her, O Lord, and let perpetual light shine upon him/her. May he/she rest in peace. Amen. May almighty God bless us with his peace and strength, the Father and the Son and the Holy Spirit.