If you put light through a fiber it will diverge severely on exiting the fiber. It is a physics problem. The only fix is to put a lens on the end of the fiber, either a separate one or lensing the fiber itself. The larger the fiber core the less divergence there will be but you will still need a lens.
This looks to be a large core fiber, something like 2 mm core diameter. This is a core diameter much bigger than you really need to transport light from a laser, especially if you are looking for a small diameter laser beam out the exit end of the fiber.
Here is the way it is normally done: Laser--->Focusing lens-->Fiber-->Collimating lens---->giving a collimated beam at the output of the fiber. The diameter of the collimated beam will depend on the focal length of the collimating lens. For a very small diameter beam (~ 1 mm diameter) you will need to use a singlemode fiber (core diameter ~3-9 microns, depending on the wavelength of hte laser), and a short focal length collimating lens (~2-5 mm focal length, which is normally done with a molded asphere lens).
Coupling to singlemode fibers from a laser requires positioning to the micron level, which is not easily done without proper equipment. You can also couple to a multimode fiber (such as a 62.5 micron core or a
100 micron core), which will make coupling into the fiber easier, but you will not be able to produce well-collimated small diameter beams at the far end of the fiber.