Got a iPhone as a gift person doesn't remember there Apple ID and password. How to solve that?

See if they can recover the ID/password.

Apple ID - How to find your Apple         An iCloud e-mail address is an Apple ID.

Apple ID - Find

Enter the Apple (iCloud) ID and click Forgot Password.

Apple ID - Manage

Apple ID – Forgot Password

If necessary, if they are the original owner, have them take the device, the original purchase receipt with the serial number, and a photo ID to the nearest Apple Store.

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or contact Apple ID Support. They will need to see the original purchase receipt/paperwork also.

Apple ID Support

Apple ID Support (2) 

Apple Support by e-mail or chat         

Apple Support using Twitter

Or fill out and submit this form.

Show that person this link Turn off Activation Lock - Apple Support the section about forgot.