A share of XYZ is a share of XYZ. The only differ

A share of XYZ is a share of XYZ. The only difference from a holder's point of view is the date of purchase and price of purchase. The option allowed to the account holder in choosing cost basis method for stocks, among the three methods offered, became available after Jan 1, 2011. That was the starting date for all brokers to report cost basis of stocks their customers purchased after 01/01/2011 directly to IRS. Up to that date, the buyer not the broker had the obligation of reporting cost basis to same; before that date, brokers had been reporting customer stock sales and amounts received. 

If you search the broker website, you'll find information on choosing cost basis method. The usual default is FIFO, but it's good to double check.