Remain obscure.
Indeed!
"Then went outside"----maybe Mr Oswald meant the Depository roof?
"to watch"----maybe Mr Oswald went up to the roof to pick up his watch which he had left there earlier in the day?
"P. Parade"----maybe "Parade" is actually "Paracle", i.e. short for "Paraclete"?
In short, it is at least as likely that Mr Oswald told Captain Fritz he
slipped up to the roof to pick up his watch and meditate p[rayerfully on the] Paracle[te]'s promise that time could be transcended as that Mr Oswald told Captain Fritz he
went outside to watch the Presidential parade.
If only Agent Hosty had used
clear language!