For fuel buyers, free. Connect QuickBooks Online on Settings > Integrations and each charge you approve becomes a bill from the carrier in QuickBooks.

What syncs

You approve a charge: a bill from the carrier for exactly the approved amount, dated the day you approved it. Bill no. is the carrier's invoice number, the memo has the record number, terminal, date, billed time and a link to the record, and the invoice PDF is attached.
You pay in Demurly: a bill payment against that bill, from your payment account (a check, or a credit card payment when the payment account is a credit card account).
You pay the bill in QuickBooks: within about 10 minutes the charge shows as paid outside Demurly (with the QuickBooks payment's check number), and the carrier confirms the money arrived.
On the record, a line says where it is: "In QuickBooks as Bill 1042".

Set it up

Settings > Integrations > QuickBooks Online > Connect, and sign in at Intuit as a QuickBooks company admin (or a user who can add bills, vendors and attachments).
On the QuickBooks bills card, map each carrier to its vendor: Pick vendor, search by name, Use this vendor. Or turn on Create vendors and Demurly adds the carrier as a new vendor.
Optional: Expense account (the account's name, number or ID; empty uses the account on the vendor's last bill), Payment account (empty uses your only bank account) and Payment terms in days (empty uses the carrier's invoice due date). Save bill settings.
Switches: Create bills for approved charges, Create vendors, Skip charges a carrier also sends by EDI 210, Check for bills paid in QuickBooks.
Charges approved before you connected: Bill earlier charges, pick a start date, and see how many it will bill first. Charges you already paid are left out unless you tick Also bill charges you already paid (then each is billed and its payment recorded).

What doesn't sync

Bills you change or delete in QuickBooks aren't changed in Demurly; a voided or deleted bill is noted on the record and the charge is left as it is.
Tax codes, classes, locations and approval workflows aren't set by Demurly.
QuickBooks Desktop isn't supported.

Troubleshooting

"Waiting for a vendor mapping": pick the carrier's vendor on the bills card; the waiting bills go in right away.
"QuickBooks has no account …" or "… is a Bank account; bills need an expense account": fix Expense account, then Retry.
"This vendor has no earlier bill in QuickBooks to take an expense account from": set Expense account, then Retry.
"QuickBooks has more than one bank account" or "no bank account": set Payment account to the one Demurly payments come from.
"QuickBooks already has bill … from this vendor that isn't this record's": another bill uses that number. Check it in QuickBooks (or turn off "Warn if duplicate bill number is used"), then Retry.
"… totals $…, not the approved $…": tax or a line was added in QuickBooks. Fix the bill there, then Retry.
"QuickBooks didn't answer …; trying again later": Demurly tries again by itself.