Shalom and thank you for your question! It is permissible to remove the abandoned objects, and we will examine this scenario in greater detail from the perspective of Halacha. If there is reason to believe that the former occupants of the office might still want these objects, despite having been warned, one is not allowed to take possession of them, just to move them temporarily.
The Halachic reasoning is as follows:
In a case where people put their possessions into a particular place without having received permission to do so, there are different opinions amongst the codifiers as to whether or not they need to be notified before their possessions are removed. In the case of a person who enters a synagogue to learn with his own books, but thereafter leaves them there, the codifiers again differ as to whether or not this is considered as leaving possessions without permission.
Rabbi Moshe Feinstein cites the debate between the Rambam (Maimonides) and the Rash, (Rabbi Asher Ben Yechiel,) concerning an incident where a room was rented for the purpose of storing etrogim boxes, and they had still not been removed by the end of two years. Since the renter placed the boxes in the room initially with permission, but thereafter left them there without permission, the law is like in a case where someone leaves fruit in his friend’s home without permission. The Pitchei Teshuvah, (87:1) disagrees, saying that one cannot compare a person who doesn’t reclaim an object that he deposited originally WITH permission to a person who placed something in his fellow’s yard without permission. Since it was originally with permission, the person who owns the place is not allowed to dispose of those possessions.
Thus, regarding possessions in public places whose owners have not reclaimed them, since the original placement was WITH permission, the owner of the place where they were put cannot throw them out.
Rabbi Moshe Feinstein however, maintains that it resembles the case of someone placing things in his friend’s home without permission, in which case the Remah says they cannot be removed without letting the owners know, and those who decide according to the Rambam debate whether or not to notify the owner.
Removing the possessions to a public domain seems to be unanimously frowned upon. According to the opinion of the Pitchei Teshuvah one may not throw away the possessions without notifying the owners since originally they were brought with permission.
The codifiers suggest that a sign be made stating that it is forbidden to leave possessions behind in that place, and that possessions left behind will be free for anyone to take.
This course of action brings together both opinions because according to the Rambam the possessions can be removed without prior notice, while according to the opinion of the Rash, the notice is sufficient warning.
In summary, it is permissible to remove the abandoned possessions, (unless they are items of value that the owners are likely to want to reclaim,) but since there were prior warnings, they may be temporarily removed.