Problem with Neo 6M and Arduino Mega 2560

It works just perfekt!

Adjusting your code to this:

//gps test
// connect GPS TX to Mega pin 19 (RX1)  GPS RX not connected
#include <TinyGPS++.h>

// The TinyGPS++ object
TinyGPSPlus gps;

void setup()
{
   // Open serial communications
   Serial.begin(9600);  
   Serial1.begin(9600);
   //Serial.print("Mega up");
}

void loop(){
  // This sketch displays information every time a new sentence is correctly encoded.
  while (Serial1.available() > 0){
    gps.encode(Serial1.read());
    if (gps.location.isUpdated()){
      Serial.print("Latitude= "); 
      Serial.println(gps.location.lat(), 6);
      Serial.print(" Longitude= "); 
      Serial.println(gps.location.lng(), 6);
    }
  }
}

Gives me:

 Longitude= X.XXXX21
Latitude= XX.XX890
...

I've read the limitations section in the library description.

Can you please explain it to me, why you decided to connect the GPS TX to 19(RX of the Mega) and don't connect the GPS RX to any pin? Whats the theory behind this? @groundFungus

Thank you so much!
Marc