In general:
If your mother (or her estate) donates an item of tangible personal property, the donation value is equal to the cost basis for items owned for 1 year or less. For items owned more than 1 year, the donation value is equal to the cost basis unless the item is used for a "related" purpose. For example, if she donates antique furniture that she bought 70 years ago for $50 to a museum that will study and display it, she can claim FMV, but if she donates it to public television to be auctioned for a fundraiser, she can only claim her basis. Also, if the charity disposes of the property within 1 year, they must report the disposal on form 8282 and describe how the use of the property contributed to the organization's charitable purpose.
However, if you have inherited the property, you inherit a stepped-up cost basis equal to the FMV on the date of her death. If you donate the antique furniture, you get the same value of deduction whether you donate it for a related or unrelated purpose.
Now, this medication is a type of "tangible personal property" although somewhat different from a piece of furniture or used books, and your specific donation raises several concerns. For example, did the manufacturer's grant program have a clawback option if your mother was unable to use the medication? Is it even legal to donate "used" medication in your state? How would someone verify it was useful, not contaminated and not expired? Who would be legally authorized to accept the donation and dispense this medication (there might have to be a licensed pharmacist involved)? Then, what is the actual FMV? The manufacturers' list price, the co-pay that someone with decent insurance would pay, or something in between?
And it sounds like you are aware that for a donation over $5000, you would need a signature of a qualified appraiser and a signature of a responsible official from a charity on an original form 8283, that you will mail to the IRS after e-filing the rest of your return.
