The cost basis of property transferred at death receives a “step-up” in basis to its fair market value. This eliminates an heir's capital gains tax liability on appreciation in the property's value that occurred during the decedent's lifetime. That is, if you sold the mutual funds, after inheriting the account, there is likely very little capital gain or loss.
Most, if not all, capital gains distributions from mutual funds (box 2a of the 1099-Div) are paid in December, so those are all yours. They are correct, they only send one 1099-Div for the entire year. Dividends are usually paid monthly or (more likely) quarterly (but some are paid only in December). You'll have to use the mutual fund statement to allocate those.
