I believe this is the paper:

http://pubs.acs.org/doi/full/10.1021/acsenergylett.6b00029

The headline, while not outright lying, is clearly playing on ambiguity to suggest a more sensational story

The "student" is a doctoral student with multiple previous publications (and not, say, a 17 year old high school student)

"Lasts 400 years" refers to the battery's potential ability to withstand a very high number of recharge cycles while maintaining capacity (and not, say, that it can supply energy from a single charge for 400 years)