The general rule is that any distributions made to the beneficiaries during the tax year are deemed to be income from the trust first and then principal to the extent the distributions exceed the trust income for the tax year.
For example, if the trust has $50 of interest income and $25 of dividends for the year and makes distributions of $150 to the beneficiaries, then the $150 distribution is deemed to be $50 of interest, $25 of dividends, and $75 of principal. The trust then gets a $75 deduction on its income tax return for the year (Form 1041) and it reports the income to the beneficiaries via Form K-1. The beneficiaries then report the income on their personal income tax returns (Form 1040), pro rata. The income that becomes taxable to the beneficiaries retains the same character to the beneficiaries as it was to the trust; i.e., dividends to the trust remain dividends to the beneficiaries, etc.
So, any income from the annuity that was received by the trust during the year will be deemed to have been distributed to the beneficiaries during that year, to the extent of the distribution.
You should be aware, also, that your mother-in-law's annuity may consist of dividends and/or other types of income that was never taxed to your mother-in-law during her lifetime. That untaxed income does not vanish upon her death. Instead, it becomes taxable to the beneficiary(ies) when the annuity is surrendered. This type of income is called "Income in Respect of a Decedent" or "IRD" - in other words, this type of income does not get a step-up in basis upon the death of the owner, as does real estate and other assets. The insurance company should issue a Form 1099 at year end that tells you the amount of the distribution and the amount that represents taxable income.