This is the 5436th most frequent Japanese word.
あげれ
A potential or colloquial form of the verb "あげる" (to give, to raise), meaning "can give" or "can raise."
The word あげれます is used here to indicate the ability or possibility to give something, emphasizing capacity.
私は彼のためにプレゼントをあげれます。
I can give him a present.
In this context, あげれますか represents the polite inquiry about an action involving giving or sharing thoughts.
その本を読んだ後に私に感想をあげれますか？
Can you share your thoughts with me after reading the book?
Here, あげれて implies a completed action where giving assistance was successfully accomplished.