The sentence you gave is almost perfect! Here's a corrected version with small grammar improvements:
Original: Jays make food caches in different places and often forget where. These forgotten acorns and hazelnuts can grow into new plants and trees, making the forest bigger and healthier.
Corrected: Jays make food caches in different places and often forget where they put them. These forgotten acorns and hazelnuts can grow into new plants and trees, making the forest bigger and healthier.
Explanation: We added "they put them" to make the sentence clearer and grammatically complete. Otherwise, the sentence is great and easy to understand!