@Karpivna, the Home Army (Armia Krajowa) was a resistance in occupied Poland. Polish Army (Wojsko Polskie) was a regular army – those who remained in Poland formed the resistance groups, the others went on exile to form the armed forces out there to help the Allies. AK was recognised as the Polish army in the Polish Underground State, though. Naturally, not only the soldiers were members of the resistance, civilians were joining too.
In other words, when the Germans with their Soviet friends occupied Poland, the regular army stopped to exist here, so various resistance groups were formed – AK was the largest, which cultivated the traditions of Wojsko Polskie. As Armia Krajowa it functioned since 1942, but before it was known under the name Związek Walki Zbrojnej (Union of Armed Struggle).
Here’s about the Polish Armed Forces (section about WW2) from Wikipedia:
“At the onset of World War II, on 1 September 1939 Nazi Germany invaded Poland. Polish forces were overwhelmed by the German attack in September 1939, which was followed on 17 September 1939 by an invasion by the Soviet Union. Some Polish forces escaped from their occupied, divided country, and joined Allied forces fighting in other theatres while those that remained in Poland splintered into guerilla units of the Armia Krajowa (“Home Army”) and other partisan groups which fought in clandestine ways against the foreign occupiers of Poland. Thus there were three threads to Polish armed forces from 1939; the Polish Armed Forces in the West, the Armia Krajowa and other resistance organisations fighting the Germans in Poland, and the Polish Armed Forces in the East, which later became the post-war communist Polish People’s Army (LWP).”
I’m pretty sure mentioned Jacob joined Armia Krajowa or any other resistance group, since UPA didn’t exist in 1939.