Thankfully, I reached my husband who had just dropped us off immediately. Thankfully, the friendly agent called the State Police barracks at Logan and found a trooper on duty who was a notary public. Thankfully, the trooper agreed to write the necessary letter. But he was in a far terminal and the clock was ticking.
Schlepping our bags, my daughter and I ran for the airport shuttle bus, which finally came and, after an excruciating process of dropping others off at their terminals, let us off at ours. After a cross-examination of me and my daughter in person, and my husband over the phone, the trooper wrote and stamped the letter. We once again ran for the shuttle. By the time we got through security, our plane was boarding. The gate agent gave our letter a cursory glance.
Since then, whenever friends leave the country with a minor child, I remind them to check the airline and country policy regarding parental consent.
P.S. The trip was wonderful.