It was suggested elsewhere that all 39 would go to Southern, allowing a similar amount of 377/1s to join Southeastern, with some of the not at all intensively used 717 fleet working a few of the more lightly loaded current 700 workings out of King's Cross. A handful of 700s would then support the 379s on Ely services. I can't remember where I saw that now.
I'm keen to know if Southeastern actually plan to give their 377s their own interior. They put so much work into making the 375s nice inside, but then received the 377/5s and just left them with absolutely filthy green seat covers and Southern blue walls and panels. The 377/1s won't be filthy thanks to the refurbishment, but they will be off brand.
Only in the pernickety interests of neatness and consistency, if GTR
did become in a position to give Southeastern around 40 377/1s, it's a shame they couldn't instead hand over
all 64 377/1s and therefore take
their 377/5s (there's 23 so it works!), meaning both TOCs would have a whole subclass rather than half and half.
I suppose there's little merit in that for SE as the 377/1s have three different layouts among them anyway, so that's not really a serious suggestion that I'd believe to be beneficial, just me being unusually a little OCD there