If it is the oil cooler it is the whole cooler and not the the coolant pipe that connects the cooler to the block. You can see from the first link that MaxRS6 posted that the coolant pipe is separate from the oil passages. The oil/coolant can't mix there, just in the cooler itself if it is the cooler.

I don't know of any gearbox/engine coolant cooler that we have.

Any coolant in the oil? Should look like milk chocolate.

Don't drive it until you nail down what it is or at least confirm no coolant in the oil. Most likely the repair will start with "first, remove the motor"