I am sorry for your loss.
You should seek guidance from a legal/tax professional since the figures here are large.
Note that the trust would typically take the property with a stepped up basis and prior accumulated depreciation (prior to your mother's passing) would essentially disappear. Depreciation would start over with the new, stepped-up basis.
Whether or not the trust actually receives the stepped up basis is dependent upon the type of trust and how the property was held prior to her passing.
Regardless, if the trust files a final return, the income (rent) and depreciation for that two-month period could be passed through to the beneficiary on the K-1.
