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So, for the purpose of bringing the boom... you don't consider when the blinking character "return(s) to an unoccupied space of (his/her) choice" that it was movement?
No, the spell only lasts 1 turn, it can not affect the other character in the second turn:
Round 1
- PC1: Booming Blade
- PC2: Blinks at the end of his turn.
Round 2
- PC1: Booming blade ends and he can not attack PC2.
And movement is defined on the combat section, you need to use your speed points.