I've forgot to tell you that I've tried with SQL Management Studio using the GUI and when I import the backup on the new machine I can't see the data of the last 4 months.
Do your method export all the data in the DB backup?
what do you mean by cannot see the data of the last 4 months?? a full backup will inculde all the data present in the database at the time it was finished.
if you restore the backup/backups - all you would get is retrieve the data that is present in the backup file.
so, if the data you were looking for was already DELETED before the backup was taken on the source system, it will not inculde that information,(assuming a simple scenerio of restoring a full backup),so, there is no point in restoring the backup.
if you looking to restore certain data, you will need to figure when the data was present in the source system, and if you have those backup files , you would need to restore them.
msdb.dbo.backupset table has all the information on when backups taken and type of backup etc..