Gifts received from anyone, in ANY AMOUNT of ANY KIND  are NOT taxable income  to the recipient of the gift and are not reported on your annual income tax return. 

The $15,000 threshold is for whether the GIVER of the gift has to file a gift tax return.  "Gift Tax" is somewhat of a misnomer.  Even though a gift tax return may be required, for individual  gifts over $15,000, very few people ever actually pay federal gift tax. The purpose of the gift tax return is usually only to document a reduction in the allowable estate tax exemption.
See https://turbotax.intuit.com/tax-tools/tax-tips/Tax-Planning-and-Checklists/The-Gift-Tax-Made-Simple/...  

Now when you SELL the stock you will report the sale so you must know the donor's basis  AND  the fair market value of the gift as of the date of the gifting ... get them both asap.

The general rule is that your basis in the property is the same as the basis of the donor. For example, if you were given stock that the donor had purchased for $10 per share (and that was his/her basis), and you later sold it for $100 per share, you would pay income tax on a gain of $90 per share.   Read the rules here : 

https://www.irs.gov/faqs/capital-gains-losses-and-sale-of-home/property-basis-sale-of-home-etc/prope...