You'll probably need to take the end cap off. It's tricky to get all four brushes pushed back to slip it over the armature without the plastic ring made for the job (it comes with some aftermarket brush assemblies to make the install easy), but you can do it if you hold the brushes back using two fingers from each hand on either side, holding the brushes back with a fingertip on only half the brush, letting the other half clamp onto the armature, then just slide it on the rest of the way. Either that or find a plastic cap or wooden dowel the same diameter as the inner part of the brush assembly, use that to hold the brushes back, slip it over the armature, and slowly slide it back to let the brushes click against the armature, but without messing them up. They are pretty soft and will chunk or lose material if scrubbed with something rough. They'll still work ok, but every tiny bit of material they lose is less electrical contact and less electricity getting to the starter, so less torque.
Before you put the starter back together though, look at it and make sure all the magnets (the curved black things inside the metal housing and around the inner copper armature) are stuck on there good. The magnets should not move and should not have any cracks, or otherwise be damaged. If there's any damage to anything inside the starter, that will prevent it from spinning and so the solenoid will just click but the starter can't use the electrical energy to do anything if it's stuck, or at the very least will be noisy after awhile of starting with loose parts inside.
Since Ford vehicles have two starter solenoids (one at the fender near the battery, one on the starter) you need to be sure they are both good, sometimes the fender relay goes and it's the only original part left in the system but nobody suspects it. If it works fine with the other starter though, that should mean the fender relay is good and the relay on the starter might be bad.
You might also want to check the battery cables, in particular the ends near the battery for green/blue on the copper wire showing corrosion, and check the ground point for the negative wire on the frame and at the engine block. It's rare that a bad ground is the cause, but the combo of old corroded cables, a rusty crusty frame ground, and an oily wet engine block ground can be enough to make a starter click instead of spin.
If there are no starting issues with the other starter on there for now, then it's likely just something to do with the starter, possibly the solenoid. I haven't heard of too many issues with them, even on the cheapo China-made gold zinc ones, but there are plenty of vehicles where the cheapo solenoids on the starters constantly go bad, but the solenoid costs about as much as a starter, so it's cheaper/easier to just keep replacing the starter.
You should also be sure the small positive wire to the starter solenoid is on there good - if it's loose (which is why they went from the spade terminal to the stud terminal, some spade connectors were never pushed all the way on, so a lot of 'starter problems' were just DIYers or techs that didn't push the terminal on enough or where the female spade connector was loose and just never adjusted with pliers to clamp on tight to the male terminal) it won't make a good connection and again, it'll be enough of a connection to make it click but not enough to spin.
