This is really not that complicated. First, a tribunal would not investigate the validity of the first marriage, since the Respondent party is now dead. It’s impossible, basically, since there is no way to initiate a case when there can be no citation of the Respondent party.
Second, if there is no obvious reason, apparent in documentation, to question the validity of that first marriage (for example, one party was previously married) the Tribunal will operate on the presumption that it is valid and impeded any subsequent marriages of either party, until the death of the wife. The man’s prior bond would be the ground of invalidity.
Third, the second and third marriages also enjoy a certain presumption of validity since they were “properly celebrated” (in accord with the form required of the Parties). So, in order to declare them invalid, the documentary process would be used.
Fourth, the subsequent marriages would not convalidate since the man and his second and third “wives” were not living as a married couple when the death occurred. If he was living with either of them when the first wife died, then it could be argued that the marriage became valid when the impediment ceased. He was not living with either of them, though, and so the marital consent no longer existed. There could have been no convalidation.
I recall a similar thread on this topic, by the same OP… But, sometimes it helps to reinvent the wheel.
Dan