Is it permissible to take a cash amount from a friend in exchange for a bank check that will be deposited into his company, due to the unavailability of liquidity to withdraw funds from the bank?

If taking the cash amount and giving a bank check is for the purpose of currency exchange (sarf), then actual possession (qabd) must occur. This is achieved by genuinely transferring the amount from your account to the company's account, or by giving a certified check. However, merely receiving an uncertified check is not considered constructive possession.

If your friend is an agent, then what he does must be authorized by his employer.

But if the transaction between you is a loan, then there is no harm in it, and the check would serve as a means of documentation, provided that your friend is authorized to do so.