To really test the FBG you'll need to know what wavelength they are designed for and couple laser light into the fiber. Preferably you'd use the correct optics with similar numerical aperture and measure the relative intensity and the spectral output. Note that most FBG are used in single mode fibers which have low numerical aperture and are hard to couple light into if you don't have the right optics/mounts. If you're working in the infrared at telecomm wavelengths connectors and test fixtures are much much cheaper.
If you're ok with not testing them at the wavelengths they're designed for and just want to see if there is a break in the fiber couple in a visible laser diode and look for any hotspots or light leaking out which is indicative of a break in the fiber:
Choose a wavelength that's somewhat transmissive based on the transmission spectrum of the array. Since there are fc connectors on the end the easiest way to do this would be to buy an fc mounted lens designed to focus light into the fiber (although it won't be perfect because you'll be using the wrong wavelength). Mount the collimated laser diode source, couple light into it into the fiber and look for any obvious leakage out of the fiber. You might be able to couple enough light in without a lens although I wouldn't count on it. If the laser is eye safe in a dark room then turn off the lights and let your eyes adjust.
If you happen to have a spectrometer laying around you could characterize any broadband source you have then couple light from the source into the bragg grating and look at the output. Any peaks missing would be indicative of an reflection line. However, assuming this bragg grating is single mode (~5µm diameter core) this probably won't be very efficient and you might struggle to get enough light through the small fiber. Also, if you're out at the telecomm wavelengths (~1550nm) most spectrometers aren't designed to go out this far and won't work well or at all. If you can provide more specifics such as design spectrum, fiber length, core diameter someone might have some bright ideas.
Any limitation in your fibre will be inconsequential compared to those in your optical modulation/demodulation processes.
You will have to look critically at the characteristics of your incoming signal to decide what sort of optical modulation scheme will best preserve the parameters you want to keep, and which you can allow to degrade.
If it's a data signal, you may want to throw away weak carriers. If it's a spectrum scan, you may want to keep weak ones, and ensure that strong nearby signals generate don't obscure them with intermodulation.
The most conceptually straightforward way to encode an RF signal onto optics is to analogue AM modulate a subcarrier, which has a frequency of several times your bandwidth. However, the linearity of this could vary between bad and very bad, which would affect your EVM slightly, and your co-channel hugely, if such things are of consequence in your original signal.
An ideal route would be to fully demodulate your signal, assuming it to be data, and ship the data along the fibre, using a standard data format and end-point chipsets.
There is not enough use-case information in your question to answer more than very generally at the moment. Depending on your field of employment, you may not be able to give out use case information!
Best Answer
Try this. Put a cable between the transceiver and the receiver. Then connect a spdt switch to the transceiver's vin. The other two ends of the switch go to vcc and ground. Flip the switch, make sure the transmitter led is turning on, and then use a multimeter to test the vout pin on the receiver.
simulate this circuit – Schematic created using CircuitLab
This will tell you if the two are working. Even better, a very slow clock that you can measure would work as well. A 555 chip set up for 2hz connected to vin should cause vout to switch on and off two times a second (See: https://electronics.stackexchange.com/a/64527/17178)