Hello
I finally found the answer.
The TinyGPS++ is providing lat/long with the gps.location.lat() & gps.location.lng() in decimal degrees ( (DD) : 41.40338, 2.17403)
But IGC files need coordinates in degrees and decimal minutes ( (DMM) 41 24.2028, 2 10.4418).
To move from one to the other you have to multiply the decimal by 60!
41.40338 ==> 40338 *60 = ==> 2420280 => 41 24.2028
have fun!
Inspiration here : Trouver des coordonnées ou effectuer une recherche par latitude et longitude - Android - Aide Google Maps
G