Sounds like he's paid for the ticket. If so, he decides what to do with it. Unless your daughter was the one who broke up with him. Perhaps she told him he couldn't.go. I don't have enough information to have an idea of what would be best in your situation.
I know your question is about the airline ticket. I see reasons to not get into this situation. As you've learned, relationships at this age are rarely stable.
Rarely does anyone stay with their first serious boyfriend/girlfriend. Dating is to learn about themselves and relationships. I wouldn't agree to include a boyfriend unless they had been comfortably dating, without fights, for at least 6 months, were both mature, had spent enough time with me that I believed all of us would have a good time and trip was such that if vacation was not going well, I could separate them. The trip would be local, in the USA.
When vacationing overseas there is no way out if trip isn't working. Their breakup indicates to me, that they don't have a stable relationship. What would you do if the breakup happened while on vacation.
Life especially while on vacation in a foreign land, is stressful. Not everyone is able to make adjustments to different culture and the time difference. I was always a bit tired and confused. Fortunately, their break up happened at home.
I've experienced that teens spend very little time with families. It's likely she would spend most of her time focused on her boyfriend. Being together 24-7 is stressful. How will your daughter and boyfriend handle that stress? Fight or sulk? Trips have too much closeness. As an adult, I went on vacation with a male friend. Both of us were unhappy and broke up when we got home.
Have you taken an overseas trip before? I have and the transition took a lot of energy to adjust to the time difference and the different culture; to always be on the go wanting to see as much as I could.
Whether or not to help with airline ticket depends on what you told him about his responsibility for the ticket and how the break up happened. Most breakups involve both people. No one person is at fault. If that's your daughter's breakup, I would expect my daughter to pay half. Not you. Your daughter.l