My understanding is that a departed soul takes a new birth according to the karma and lose identity with the previous birth and contact with the off springs .
If this understanding is correct how do they become our pithrus and who accepts our offerings performed during Pithrupaksha?
Only our ancestors who have not yet taken a new earthly body and are living in different lokas, particularly the pitriloka, take our offerings. Ancestors who have attained liberation or have been born in a different bodies do not get the offerings. One reason for giving the offerings is that these ancestors in pitriloka should exhaust their karmas and either get liberation or take birth to completely exhaust their karmas.
WIth best wishes,