I found my moms old Apple Watch and it has activation lock and not same Apple ID how to I connect it to my phone

See -> How to remove Activation Lock

How to remove Activation Lock – Apple Support (UK)

• If you need help removing Activation Lock and have proof of purchase documentation, you can start an Activation Lock support request.

You can also contact Apple support for help, -> Get Support (apple.com)

You have to show proof of ownership of your product, provide all documentation showing your purchase of the device.

If you do not have additional proof of ownership, contact the reseller. They may be able to provide the original purchase document.

Once Apple receive your proof of ownership, Apple will further review your request and provide an update.