All perfect praise is due to Allah The Lord of The Worlds. Blessings and peace be upon Prophet Mohammad.
The briefcase that you have found is a lost property, so you should make a public announcement about it in places close to the area where passengers take taxies and get off them. You should also check with the police station or the travel stations about the proper way for making an announcement about it. If finding its owner was a hopeless endeavor, then give it or its value as a Sadaqa (charity) for public interest. However, it is impermissible for you to benefit from it as it doesn`t take the ruling of Luqatah (Found article), rather, it takes the ruling of “ Lost property. “
It is stated in [Nehayat Al-Mohtajj] ,a Shafite book: “The bottom line is that this is a lost property, so if he didn`t give up hope in finding its owner, then he should keep it along with making announcements about it, or he should hand it to the judge for safe keeping, and whenever the latter gives up on finding its owner, it becomes part of the treasury as is the case with the state-owned land, and so it is disposed of by the state even for building a mosque.” To understand the difference between the Luqatah and the lost property, we report what Al-Khateb Ashirbini said in this regard: “If the wind carried a piece of clothing into his lap, for example, or a runaway threw a sack into his lap, and he didn`t recognize that runaway, then it is a lost property which he is obliged to keep, but not to own. Muslim scholars differentiated between the Luqatah and the lost property as follows: Lost property is that which is kept in a place that suits it such as the items kept in places overseen by the state and the like, and whose owner wasn`t known. As for the Luqatah, it is that which was found fallen away from its usual keeping place. This ruling applies in most cases.” And Allah Knows Best.