I finally found a solution that works 100%. Please refer to github project https://github.com/klinker41/android-smsmms. (Anyone who find it usefull please donate to author http://forum.xda-developers.com/showthread.php?t=2222703).
Notice, that obligatory settings are only
Settings sendSettings = new Settings();
sendSettings.setMmsc(mmsc);
sendSettings.setProxy(proxy);
sendSettings.setPort(port);
you can get them something like (found at Set APN programmatically on Android - answear by vincent091):
Cursor cursor = null;
if (Utils.hasICS()){
cursor =SqliteWrapper.query(activity, activity.getContentResolver(),
Uri.withAppendedPath(Carriers.CONTENT_URI, "current"), APN_PROJECTION, null, null, null);
} else {
cursor = activity.getContentResolver().query(Uri.withAppendedPath(Telephony.Carriers.CONTENT_URI, "current"),
null, null, null, null);
}
cursor.moveToLast();
String type = cursor.getString(cursor.getColumnIndex(Telephony.Carriers.TYPE));
String mmsc = cursor.getString(cursor.getColumnIndex(Telephony.Carriers.MMSC));
String proxy = cursor.getString(cursor.getColumnIndex(Telephony.Carriers.MMSPROXY));
String port = cursor.getString(cursor.getColumnIndex(Telephony.Carriers.MMSPORT));
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