There is a connection between Mr. Widmore of the construction and pharmaceutical industries and Desmond. Also that his daughter, Penelope, will use her $$ to get what she wants (a baby). Remember the pregnancy test Sun used was from Widmore Labs and it was asked ‘who travels with a pregnancy test?’ – well… someone trying to get pregnant.
Now, the woman in Desmond’s photo is a dead ringer for the wife who wanted to adopt Aaron that first time (though Desmond was not the husband). Is Penelope Widmore married to Desmond and, thinking Desmond dead, either remarry or hire someone to pose as her husband in order to adopt Claire’s baby and when that didn’t work out, turned to the psychic? The LA connection works because Desmond was training/living in LA., but I don’t know why Claire HAD to be on that flight. Because it is the one that Penelope was taking? So what?
If any of this is the case, then why was she so set on Claire’s baby? Is there some circle with Desmond/Jack/Christian/Claire? There is also the issue of Claire recognizing her at some point during the trip to LA.