It appears that according to this page ..
http://www.amazon.com/HQRP-compatible-608558-001-605344-001-Replacement/dp/B005G2QZ8I
.. 608558-001 / 605344-001 / 608559-001 / 593298-001 are compatible,
but according to the manual of the laptop at ..
http://bizsupport1.austin.hp.com/bc/docs/support/SupportManual/c02666747/c02666747.pdf
.. 605344 is the right one.
However, the 608558 does look the same.
Is anyone confident the 608558 and 605344 are compatible? I have found 605344 at a reasonable price.
I currently suspect they are the same or almost the same but HP rebrands them to keep the prices up.