When Paul heard that the new converts in Thessalonica were remaining faithful, especially in the face of persecution—which was the reason he had to leave, because he was the main target of the persecution—he wanted them to know just how thankful he was for them,

For what thanks can we render to God for you, for all the joy with which we rejoice for your sake before our God, night and day praying exceedingly that we may see your face and perfect what is lacking in your faith? (1 Thessalonians 3.9–10).

When you see new converts doing well, tell them so, and pray for them endlessly, and tell them that you are praying for them without ceasing. Even mention specific things for which you pray.