Banking / Matching Bill in different currency

Banking / Matching Bill in different currency

Scenario
We've received a bill in CHF. The payment was made via our USD banking account.

What we tried
Matching the bank transaction to a bill - no matter which search criteria we use, no bill can be found. Trying to match the bank transaction to the bill via API resulted in the following error:
  1. {
    "code": 108018,
    "message": "The currency does not match in the transactions."
}
Question
How do you match bills with bank transactions in different currencies plus adding conversion fees? What workaround may exist?