sounds like she with the wrong broker. while they could be leaned on to cough up a copy of the statement (or statements if unsure of the month) needed. but for a small amount the 'research fee' they charge could easily eat up potential savings.

you know the number of shares. do you know the month of purchase? if so, just take the lowest price it traded in the month * the # of shares as a reasonable proxy for the true cost. you will most likely be overpaying but its much better than using 0 cost basis. If you don't know the month (or approximate) then use the lowest price of the year, or which time period she's comfortable with.