The words “unless otherwise agreed” limit the statutory default. The original agreement may require the author’s consent, prohibit transfer, limit the permitted transferee or contain a specific rule for a sale of the business. Those clauses should be reviewed before the right is included in a completion schedule.
The permitted use, territory, term, sublicensing and adaptation rights also matter. A transfer with the business does not expand the substance of the right. The buyer receives the position that was validly granted to the previous holder, within the limits of that agreement.
If the agreement and the rights schedule point in different directions, the issue should be resolved before signing. For a work that is central to the business, an express consent, confirmation by the rights holder or supplemental agreement may be required.