most data from one object to other is transfered with screlate links. Search for one which will be named like screlate.omcq.ocml (or it will be something similiar. I dont have system atm to check exact name).
In that links there is only one field mapping. When you chose it and click on Select field it will open new screen with all mapped fields listed. Add your field mapping for Interaction number there and save the link record.
I did search for any link records which looked something like 'screlate.ocmq.ocml' but was unable to find any. The only ones with 'ocmq' I have are 'screate.ocmq.cm3r', 'screlate.ocmq.incidents' and 'screlate.ocmq.problems'. There are none with 'ocml' in the name.
Are line items created from an event perhaps?
Or should I consider creating subroutine calling a new link record in the OCMQ format control record?
I can not check it myself until next week so not sure why it is not done as a standard method of field transition at creation from one record to another (like it is for incidents, change ....).
As a workaround you can tailor it at any place like fc (query the parent quote and grab the number from there), triggers after add of line item. But still it is workaround and I wont be able to check for something more easy untill next week.
If you are familar with fc and triggers, you can try to tailor it there.