"implications behind" is a perfectly valid phrase to use in written English.
It can be used to refer to the underlying meanings or consequences of an action, statement, or event. For example, you could say, "We must consider the implications behind the decision to close the factory."
The strategic and diplomatic implications behind the sales might forestall a political settlement.
Part of the storyteller's art has always been to conceal potent meanings and implications behind the artifice of happenstance.
Think also of the implications behind that sentence: to comply with that command there will be safety-first story-getting, meaning PR pap.
There are distasteful implications behind the statements questioning Gerrard at times this season, suggesting that he is not trying, or even trying to help Chelsea.
That anyone in 2014 would be pleading, as Coates is, to simply talk honestly about the implications behind centuries of proven history of one group oppressing another, is astonishing.
He pioneered a new strain of newspaper writing suitable to the dawning age of television: sharply rendered prose that went beyond the mere recounting of facts to explore the meaning and implications behind them.
The implication behind the proposal is that our nurses-of-tomorrow enter the profession for the wrong reason.
We also reject the implication behind your assertion that "California and Massachusetts alone have a bigger venture-capital industry than the whole of Europe".
Nationalists also resented the implication behind the Abbey project that there could ever be an Irish national literature in English, the language of the coloniser.
Mutual delight, eager crispness and bright elegance: these elements here become so idyllically fragrant that the ballet's perfection becomes an image of a lost generation — which is the implication behind the enchanting delicacy of Ravel's music.
The implication behind using the word modest as a synomym for Islamic style clothing is that any woman that doesn't wear this style is immodest and therefore open to scorn.
