The sentence has a few grammatical issues and could be made clearer. Here’s a revised version:
"The PA she spoke with during the call told G to have it paid and to provide an invoice for an investigation into who is responsible."
Changes made:
1. "through the call" changed to "during the call" for clarity.
2. Added "to" before "provide" for parallel structure in the commands.
3. Changed "who's" to "who is" for formality and clarity.