While "Junior Fullstack Developer" is his title, the developer can still have roles like "Responsible for Code Reviews for this part of the code", or "Responsible for training of new hires". There are tons of examples.
In my opinion, Titles like Junior, Senior, etc. are only useful for describing job qualifications. I've seen one company where this title also had correlation with pay levels.
Being promoted usually means "Having a different job description that is usually accompanied with more responsibility and may have an increase in pay".
Promotions are tricky. No discussion about promotion can be done in vacuum. What is your company's promotion policy? Who else might deserve a promotion that may be ahead in line? etc.
Motivation, on the other hand - that's the name of the game. You want this developer to feel motivated and we understand now that it can be done by improving the job title. My suggestion is rather than changing their title, focus on increasing their responsibilities and empowering them. Make them in charge of something, and you can easily add that as part of his job description.