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The Eleven-Is-To-One needed to bounce back to winning ways after an opening day 4-0 drubbing at the hands of Aduana Stars.
And it took Victorien Adebayor's 42nd-minute strike to claim three points in the matchday two fixture at Accra Sports Stadium.
Inter Allies took the lead through Kwabena Kyeremateng in the ninth minute but Salifu Moro netted for Bechem to restore parity on 22 minutes for the away side.
Three minutes before the interval, Allies managed to regain their lead through Adebayor.
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The victory has moved Inter Allies from bottom of the table to ninth position whiles Bechem, on the other hand, move down by one spot to sixth place.