Sophiam never truly “broke up” because Sophiam is and always has been fake.
TL;DR: Sophia and several other women were seen and associated with Liam through fall 2012–spring 2013, in the middle of Payzer 2.0 and well before Sophiam 1.0 was officially confirmed in August 2013, indicating that Sophiam has never been organic and is thus fake. Sophia is Liam’s beard. Sophiam 1.0 ended in May 2014 under suspicious circumstances, but she returned in the same month, marking the beginning of Sophiam 2.0. M!M rehired Sophia because of Weedgate 1.0, when they deployed Liam as the band spokesman for damage control, which required he have a “clean” (read: straight) persona.
On the backstory of Sophiam 1.0 and Sophiam 2.0, more after the jump.