Update:
I tried several tests and have to agree that the AltSoftSerial is much much faster than the SoftwareSerial. to transfer a String of 1400 letters the SoftwareSerial must work at 19200 Baud to successfully transfer them. AltSoftSerial managed to do the same task with 57600 Baud.
The problem has been solved so you guys can close this topic. Thanks again for the hint -dev
-dev:
Use AltSoftSerial instead of SoftwareSerial. But you have to use pins 8 & 9. If you can't use those two pins, try NeoSWSerial instead of SoftwareSerial.
How many times does it take? YOU CAN'T DO THAT.
It's not mine.You would read from Serial and write to AltSoftSerial. You could also read from AltSoftSerial and write to Serial, even at the same time. This is the BEST choice.
You could try Serial and NeoSWSerial (mine). This is the 2nd best choice.
Serial and SoftwareSerial might work, but SoftwareSerial cannot transmit and receive at the same time. Transmitting a character with SoftwareSerial prevents receiving a character on SoftwareSerial, and vice versa. At 9600, SoftwareSerial stops your Arduino from doing anything else, for 1ms at a time, when it sends or receives 1 character. This is the worst choice.