Yes - first job is to take the pellet out!!!!!!!
Congrats on a great get - the HW 50 is one of my all-time faves. The stock is actually the factory upgrade "Monte Carlo" one, which Beeman put on all his HW 50's for a couple years before the R8 came out (which was the same action with plastic piston seal, crossbolt safety, and new stock). Specie's pic show the standard slender finger-groove wood seen on most examples.
It does not have a safety and as already described, the thick brown factory grease is probably gumming up the trigger. Especially if the gun was stored standing on its butt, that stuff migrates aft and creates a right mess.
You might wanna check the breech seal, but the good news is the piston seal is leather and it's probably still in good shape. If the gun is dismantled, cleaned, and lubed it's likely good to go for many years.
Below is a shot of a Rekord trigger. 1 is the pull weight adjuster, 2 is the sear engagement adjuster that Silver Ace mentioned (a torx screw on newer guns, but may be a simple slotted one on yours), 3 is a little window where you can check the sear movement. Pushing down the rear of the big lever at the top until it clicks, will cock the trigger and let you check this stuff.