Thanks for the responses. Both my boards are working perfectly now. I'm sending a measurement every minute without trouble.
It appears that indeed the ACK settings did the trick as Jan mentioned (code is a little different from the .h file I got from Github). In comment Ruud mentions (in Dutch) that Req_ACK true/false has no effect. However, if disable Req_ACK my messages get sent correctly. With Req_ACK enabled, I get the same message multiple times.
// Ruud Req_ACK true/false lijkt geen verschil te maken
//bool Req_ACK =true;//0 = Disable ACK 1 = Enable ACK
bool Req_ACK =false;//0 = Disable ACK 1 = Enable ACK
bool ADR =false; //0 = disable ADR (Adaptive Data Rate) 1 = enable ADR (Adaptive Data Rate)