Shouldn't it be "on board *of* the ship" instead?

"Aboard" is a commonly used English word in relation to ships and other large methods of transportation. It has the same meaning as "on board" but may seem more natural. "He was on board the Titanic". "She was aboard the Titanic".

My personal opinion - but I can be wrong. You can say that something was on the Titanic or even on Titanic. On the other hand you can say that it was on board of the Titanic.

Thank you for your help and recommendation!

yes it is! :)