Payors of interest/div. need to use the identifying number of the person to whom the account is payable in reporting interest on Form 1099. If the interest is payable to an estate/trust, under Rev. Rul. 64-99(a rev. rul. has the force of law), the administrator/ executor must furnish the trust’s EIN#, not the his SSN# to the brokerage firm, the payor.
(Note; I do not exactly know what the trust situation is; however, as said, any trust that has more than $600 of income needs to file an annual tax return, except some irrevocable trusts classified as grantor trusts which do not have to file a return as long as the grantor reports all the income and expenses of the trust on his or her 1040 in his SSN#. If the trust was set up by the father, he would be the grantor and he is now deceased and I assume no longer filing a tax return, you probably need to file a return, form 1041, for the trust in the tax ID, EIN#.