Hello Tivadar
If I understand correctly, you want to reimage a Cisco Firepower 1010 to a Cisco ASA and then load the configuration from your broken ASA to the newly reimaged ASA, correct?
Reimaging between Firewpower and ASA is possible assuming you have a compatible hardware platform and ASA image. Take a look at this Cisco document that contains all of the information you need to reimage:
Once the reimaging is done, you will have a “factory reset” ASA to which you can simply upload the backup config from your old ASA (once again, assuming the ASA version numbers are compatible).
Let us know how you get along and if you need any additional help.
I hope this has been helpful
Laz