You need to read your lease and see if there is anything in it that relates to this.  You need to see if assumption or sublease is possible.  If it is, then you step in to the landlord's shoes.  My gut tells me that while the landlord can likely raise the rent, they can not charge this fee to you if you have found someone to mitigate their damages.  By that I mean if you broke the lease and walked away and they were left with no rent.  Here, they have a continuos tenant.  I would speak with a real estate attorney asap.  Good luck.