Is it permissible for a person to take a murabaha (profit-sharing) loan from a bank and sell it to his friend for cash, on condition that the friend repays it with an increase, just as the bank installments are?

If you were to buy a commodity from your friend in installments, after the bank has bought it and it truly enters into the friend's possession and guarantee, then there is no harm in that. However, if your friend were to buy a commodity from the bank, then sell it, and give you its price, and then you pay it back in installments for a higher amount, then this is a usurious and forbidden loan.