What size is the original and how big is the poster you want to make from it? At this current resolution it's pretty fuzzy to start with and will only get worse if you make it bigger. Contrary to some people's belief, even PhotoShop can't make a silk purse out of a sow's ear.
This would be the process for getting the best results:
Physically clean the original - If you don't have the original, stop. It's all a waste of time and money.
Scan it at the highest possible resolution
Edit the fingerprint out as best as can be done in PhotoShop under high magnification. Several hours time for this
Print to your desired size
This is a process description. I don't do this type of work professionally.
Dale