there is a part in the movie where prof x is showing students a video where moira mctaggert (i think she is the wife of gaurdian) is explaining a patient, and process, that honestly i wasnt paying attnetion to what it was, i didnt think it was important and i was really kicking myself at the end. i think it has something to do with using mutant cells to heal people with terminal diseases etc. all you need to know is there is a dude in a bed and he doesnt feel very well and moira is taking care of him (she is his doctor, or person who looks at his chart wearing a labcoat, however you interpret that)
anyways the way you find out jean grey is alive is that scott goes to alkali lake to cry and and shoot up some water. she comes out of the lake, kisses him, kills him, and so prof x senses this and tells wolverine and storm to go check it out. they find jean, bring her back to the mansion and it is explained that prof x knew about pheonix the whole time and kind of taught jean to keep the alter ego at bay in her subconscience. shes not happy about that, so when she wakes up she goes to the house she grew up in. prof x finds out she left and goes to where she is. they talk, prof x gets dusted.
now the credits scene spoiler. moira mctaggert is checking the chart of the dude who is in bed, and the dude in the bed wakes up and says hi to her.
oh and the dude has prof x’s voice. SHOCKING prof x is alive. no word on where cyclops went though