Many localities (Towns/Boroughs/States) have Building Codes and Regulations which forbid the fitting of motorized air extraction vents between rooms and only allow them to be fitted to vent air to outside the building.
If the room which requires ventilation does not have any outside walls a vent pipe can usually be run up through the ceiling to an external vent grille fitted into the outside wall or the roof of the building.
You should ask your local Buildings Inspector for advice about whether using a tumbledryer kit, in the way you have described, would actually be allowed.
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Install a vent fan to another room. This is very useful in the winter when the humidity must be kept high for that warm feeling.