If the the delivering broker does not provide cost basis information when transferring positions to your IBKR account, IBKR will set the acquisition date to the date the transfer is posted and the cost basis will be set to the closing price on that same date.
If your delivering broker participates in the CBRS, cost basis information is generally transmitted separate from the transfer and within 15 days of position delivery. Other brokers may submit this information manually. IBKR will update its default cost basis settings with information provided by the delivering broker, once received.
Also, there is a possibility that the contract was involved in a corporate action or option exercise during the transfer period. Review the position in question and if you still need assistance prior to placing a trade, please contact IBKR Client Services. Select Activity & Tax Reporting as the ticket category followed by Tax Forms.