Simple answer: yes. As DianeW explained, even a short lived business is allowed to deduct losses.
But taxes aren't simple. Two (maybe more) issues to consider:
1. Was this a real profit motive business or just a hobby. The deductions are handled differently. For a full explanation, see https://www.irs.gov/newsroom/hobby-or-business-irs-offers-tips-to-decide
2. What did he do with the left over inventory. if he kept it for personal use, he does get to write off the cost as a business expense. "Personal use" includes giving it away (making gifts) to friends and family.
