You may use J11 connector, but You must have common ground for this 2 device. You may get power banana from computer (then You have already common ground), You may get power from other power supply, but You must connect ground from banana and conventer.|
I wrote about 3.3V input and output, becouse, if You connect 5V signal to the banana pi uart You may distroy the chip. Pin 4 of pl2303 should be connected to 3.3v in banana pi.
I don't know, which color of Your converter is connected to each part of pl2303, becouse there is no standard...