I would highly syspectg it should "bolt right in" with no issues . . . BUT there might be some differences in the motor mount type and mounting, between the model years involved. Also, there might be some differences in the way the accessories mount to the block, which could mean that you use the '77 items with the '77 engine rather than swapping the '69 items onto the '77 block.
Otherwise, the '77 motor's compression ratio might be closer to 8.5 as the '69 motor would be 9.2? NOT a huge difference by the time it all gets to the rear wheels. Might put a few more degrees into the base timing of the '77 as long as it does not ping?
The '77 engine (if it still has it) would have electronic ignition, but the '69 distributor should go into the later motor, I would suspect (if the LAs were like the B/RB motors). Using the '69 carb should be OK, too.
With the '77 still out of the car, you might pop out the freeze plugs and replace them with new brass ones. Easier to do it out of the car than with the engine in the car!
For similar reasons, you might want to change the oil pan gasket. This can also give you an idea of what's in the pan and clean it out, for good measure.
A good idea to change the timing chain set, too. The one in there might still be good, BUT consider this an "insurance move" to ensure a LONG and trouble-free service life for the motor. Do douse the chain and sproketr in oil after you change it for lube when it initially starts.
As a part of getting things ready, change ALL of the rubber fuel lines between the tank and the carburetor with new OEM-spec (or better) fuel lines. Another "insurance move".
Just some suggestions. Your judgment call as to what you do.
Enjoy!
CBODY67