From: Rabbi Akiva Eiger
To: Unknown recipient
Rabbi Akiva Eiger maintains that a single witness who testifies the first husband died before the woman's remarriage is not believed even prospectively, because the daikya incentive is absent — she was already living with the second husband and would remain regardless. He also explores multiple grounds for leniency regarding the children's status, including that safek mamzer is permitted min haTorah and the woman's presumptive daikya before her original marriage, and conditionally offers to join a lenient ruling if his correspondent agrees.
Source: Shu"t Rabbi Akiva Eiger §125