In the billing document there are 3 exchange rates, please review:

VBRP-KURSK 
Exchange Rate for the conversion Loc.currency <-> Doc.currency.
for Price Determination
The determination of this exchange rate depends on the setting
of TVCPFLP-PFKUR in customizing copy-control

VBRK-KURRF
Exchange Rate for the conversion Loc.currency <-> Doc.currency.
For FI postings
If there is a manual entry in the sales order field VBKD-KURRF (Goto -> Header -> Accounting), then it is copied into VBRK-KURRF.
Otherwise VBRK-KURRF is determined during invoice creation.
It is supposed that manual entry has higher priority.
See the OSS note 36070.

KOMV-KKURS 
Exchange Rate for the conversion Cond.currency <-> Loc.currency
At price condition level.
It is always determined according to the Pricing date.
See the OSS notes 92613, 97487.

During VF01 the system determines the Exchange rate for FI posting
VBRK-KURRF from the currency tables according(OB08) to the billing date only if the field Exchange rate for FI posting is empty in the source sales document (VBKD-KURRF).
If the sales document has this field filled, manually or copied from a reference invoice (by copy control routine), then it is copied in the subsequent billing document. This is the standard working of the system.

The exchange rate should be based on your configuration in copy control (VTFA or VTFL) at the item category level. The choices you have are as follows:

Pricing Exchange Rate Type (V_TVCPFLP-PFKUR)
A Copy from sales order
B Price exchange rate = Accounting rate
C Exchange rate determination according to billing date
D Exchange rate determination according to pricing date
E Exchange rate determination according to current date
F Exch.rate determination accord.to date of services rendered