How to book incomes from a past accounting period?

[Jonas Wagner]

Dear Gnucash users,

a new season just started for an association I'm part of. I created a new
Gnucash file for the new season's finances.

Now I occasionally receive money that "belongs" to the past season. For
example, somebody who forgot to pay their membership fees last year pays
the double amount this year. What is the best way to handle this?

What I tried:

* Equity:Past season
  - Overdue membership fee for John Smith: $20 (to Income:Membership fees)

* Income:Membership fees
  - Overdue membership fee for John Smith: $-20 (from Equity:Past season)
  - Membership fee John Smith (past season): $20
  - Membership fee John Smith (current season) $20

This seems to work, as it leaves me with the correct total of $20 in
Income:Membership fees and somehow documents past year's money.

I think the question is more general than that, though: How to handle
transitions between accounting periods? Should I book incomes from past
years under incomes? Or are they equity? A/R? Or something else?

Thanks for your help?
Jonas