Second job

recently started a second job. What do I need to provide my employer to correct my tax code? I have received a salary from both employers. The salary from my first job was taxed, but the salary from my second job wasn't taxed because the annual gross is not up to the personal allowance, and they were not aware of my first job, which is my main job. However, when combined with my second job, my total income is more than the personal allowance. Also, note that my second job is only for 2 months.

Hi Fati A,
When you started with your second employment, did you complete a starter declaration form?
If you are being taxed by both jobs using the same tax code, this will be duplicating your allowances.
Please contact HMRC to amend your tax codes, please be aware that if your allowances have been duplicated, this may result in a shortfall of tax. Income Tax: general enquiries
Thank you. 
 

No, I didn't fill the starter declaration form. The jobs kinda started at the same time