The surest way towards a good, long term solution, is desolder the old broken connector and replace with one suited to the existing plastic sheet connector. It would be good to have precision calipers to measure the FFC cable thickness, then go to your preferred electronics supplier and search the relevant parameters. For example here are a few on digikey:
https://www.digikey.com/en/products...GSQAWgBMs+fwCuykpHLrdIDlwmmrTuUSFDcJHYiPmZxIA
https://www.digikey.com/en/products...GSQAWgBMs+fwCuykpHLrdIDlwmmrTuUSFDcJHYiPmZxIA