The latter is correct. In order to clear the title to the property to permit the transfer into the husband's living trust, an Affidavit of Death of Joint Tenant will need to be recorded along with a certified copy of the Certificate of Death for the wife.
A Trust Transfer Deed can be prepared and filed at the same time as the Affidavit, with an instruction to the Recorder to record the Affidavit first, followed by the Trust Transfer Deed.
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Good advice already provided. I would add also that with family status changes, it is a good time to verify that the current trust terms are what is desired. Often, with family status changes, trusts are adjusted to accommodate the new situation.
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