Leather splitting apart

I just got a cute Packard Bell 4RB1 that I will be restoring for my one of my daughters. The leather is pretty good in general the only problem is the flaps that closes the radio in the back are splitting. What is the best way to stabilize the flaps, I was thinking on a thin pieace of leather glued from behind. Thanks

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try Aleenes Flexible Fabric Glue found at most fabric stors

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