During Moriarty's court case, The forewoman is shown having her children threatened by Moriarty via television. This juror looks conspicuously like Hope's estranged wife, and the children shown have a remarkable similarity to the children in the photograph.
Yeah, this was a popular fan theory after the episode first aired. It's an interesting theory and puts an even darker spin on things if true.
Personally I don't think it was what the show creators where intending for us to take from this episode. If it were I think they'd have made it much clearer and more obvious.
Whilst the children look similar I don't think they could with 100% certainty said to be the same and even if they were it could be a case of prop photos being used for filming that had the same children in them - they wouldn't have expected the fans to look at them so closely.
Do we see an image of Hope's wife? I can't remember that. It has been a while since I watched the episode though.
I remember that theory going by and thinking ???? there isn't enough of the wife in the torn photo to positively match her with the juror photo, and there are 2 children in the cabbie's photo, but three in the juror's (though I suppose it could be suggested that she remarried and had a new baby with the second partner). And they don't look enough alike, at least to me... tiny blurry photos like that are just not clear enough IMO. I get that there are a million clues "hidden" in the show for the fans to tease out, but I don't think this is one of them. Time will tell of course!