Agreed. It's not clear whether the jacket you have is vintage, and whether you still have the old label. If you have the old label it's totally appropriate to have that label sewn into the new liner. If the old label is missing, it's missing.
Seems spurious to try to source a random label and then sew it into a jacket that the label was never meant to 'label'. It also misleads anyone in the future trying to 'read' the jacket, that is, to figure out who made it, when, and what hides were used. Others might disagree, but in my opinion it's more or less creating a fake history of the jacket (even if that's not your intention).
The maker of an HH jacket doesn't have a label stating it's HH? That makes zero sense...
The maker of an HH jacket doesn't have a label stating it's HH? That makes zero sense...