Seven speed free hub shifters to seven speed free hub

Hi all, just wondering if anyone one could advise, I am planning on running a gear ratio from 14, 16, 18, 20, 22, 24, 28 to a 13, 15, 17, 19, 21, 24, 28 all Shimano seven speed and was told with a little rear derailer tweaking they will work!,
Is this true?

Cheers in advanced

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