Is there an update of the wireless driver version 22.214.171.124 for my HP Elitebook 2560p?
No, there is no wireless driver update for this device. I have checked the Support page for this product, and also checked the operating systems listed on the page. The latest version of the driver is 126.96.36.199 and was release in 2013. You can check this information as well using the link posted below.
Support page: http://h20565.www2.hp.com/hpsc/swd/public/readIndex?sp4ts.oid=5071202&swLangOid=8&swEnvOid=4157