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سلام دوست عزیز
بله می توان این کار را براحتی انجام داد. اگر به خود سایت api bot تلگرام سر بزنید در قسمت FAQ گفته شده:

All service messages.
All messages from private chats with users.
All messages from channels where they are a member.
Bot admins and bots with privacy mode disabled will receive all messages except messages sent by other bots.

Bots with privacy mode enabled will receive:

Commands explicitly meant for them (e.g., /command@this_bot).
General commands from users (e.g. /start) if the bot was the last bot to send a message to the group.
Messages sent via this bot.
Replies to any messages implicitly or explicitly meant for this bot.```