while i do agree that this new friendship between emma & young jean maybe forced you have to look at all of the scenarios.
1- since jean's death how many times has she interacted with emma, saving emma, hinting to emma that there was more to come. that emma had to be prepared. of course at the time everyone assumed that was all in reference to Hope but for all we know it went beyond hope and now we have teen jean.
2- emma has tasted the power of the phoenix force, knows what i can do and what it did to jean.
3- emma at the most part has limited control over her powers, with teen jean gaining powers she never had before maybe emma is using jean as a way to reclaim her previous powers as well as amplify them. as of late we know emma has been feeding off of not only teen jean's power but the cuckoos as well, who knows what the long term effects of this will be.
4- between Jean & the cuckoos emma is making sure they are strong enough to handle the telepathic responsibilities that 616 jean, xavier & herself once handled.
5- teen jean is a timebomb.... why would emma want anyone else teaching her. yes there are other telepaths out there that are stronger than emma was but not all of them have the fine-tuning and control emma has. the only other telepath that emma would have felt comfortable enough with training teen jean is xavier but he is dead
6- we have seen that the O5 can directly effect their present counter-parts in certain ways, maybe emma feels that establishing a friendship with teen jean will change her & 616 jean's stance/friendship should she ever return or atleast if the O5's return to their original place in time does change the present surrounding the x-men/mutants maybe it will better emma & jean's or even scott's relationship