USA Questions on Debit & Credit Journal Entries.

[Jasmine2018]

I have a situation where our inter-company short pay one of our invoices then they turn around and billed us in the amount that they were short paid us. I need help to make sure that I book them correctly. I appreciate very much for your help.

Two sister companies A&B, Company A back charge Company B for Consultant Fees for the month of July 2018 in the amount of 20K. Company A record:
Debit Inter-Company AR $20k
Credit Inter-Company AP (20k) (is this entry correct?) Yes, No

Company A received Payment from Company B in the amount of 10K. Company A record:
Debit Cash $10k
Credit Inter-Company AR $10k (is this entry correct?) Yes, No

Company A received an invoice from Company B in the amount of 10K. Company A record:
Debit Consultant Fee Expense $10k
Credit Inter-Company AP $10k (is this entry correct?) Yes, No

Company A issued a credit memo for Company B in the amount of 10k (the amount that Company B short paid). Company A record:
Debit Inter-Company AP $10k
Credit Inter-Company AR $10k (is this entry correct?) Yes, No

Company A issued the credit memo in the amount of $10k, this credit will offset the invoice that Company B billed Company A. It is a wash. Do I need any Journal Entry when I apply the credit against the invoice?
Please advise.
Thank you.