I'm afraid not. The Early and Late 2011 13" MBPs can use the same display panel, but the Mid 2012 (and later) 13" use a different panel. The graphics processor on the logic board went from Intel HD Graphics 3000 in 2011 to Intel HD Graphics 4000 in 2012, so my guess is that there was also a change in the display cable, and possibly the logic board connector.
Early 2011 13" MacBook Pro
Mid 2012 13" MacBook Pro
That said, it might be worth looking at the display installation guides for each model, to see if the connector falls in the same position on each logic board. iFixit doesn't stock the LVDS cable as a separate item, but Powerbookmedic lists different LVDS cables for the 2011 and 2012 models.
MacBook Pro 13" Unibody Early 2011 Display Replacement
MacBook Pro 13" Unibody Mid 2012 Display Replacement
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