Silvaire, the OP clearly stated that the engine was coming up to 2000 hrs TBO. You are well aware that under FAR, the engine can be operated under the tag - 'on condition', long after the recommended life/hours mandate, and ASSUMING that the correct FAA annual checks, 100 hour checks, are all complied with in line with the manufacturers maintenance manual, then yes - it can be 'stuck on condition'.
Obviously the engine must be thoroughly checked, at every maintenance juncture, that is only good and clever practice, but, only FAR allows this. He could not do it under EASA.