MasterBlack :
Family member wanted longer battery life.
Well, you came here for the brutal truth. You got sucked in by third party battery claim.
Third party vendors often inflate their battery capacity claims, they throw you terms like 10 cells blah-blah and you fall for it.
Third party vendors have not found a miracle battery technology, a special formulation, and able to sell you at a discount... if they did, the laptop makers would had offered you that battery technology, because they are always fighting for your business to buy their laptops. The ONLY superior battery technology is ION Polymer, which can be shaped into anything, not just round cells like what the third parties are selling you.
Short answer: You cannot get longer run...