iPhone 6 Plus denied to connect with "activation server" ???

You need to have a SIM inserted in the iPhone to activate. You cannot activate with wi-fi without a SIM.

Official Apple process:

1. Restart your iPhone.
2. If you're using a cellular-data connection, connect to a reliable Wi-Fi network instead.
3. If you get an error message on your iPhone that says the activation server is temporarily unavailable or cannot be reached when trying to activate, wait a few minutes, then repeat the previous steps.

If you still can't activate your iPhone, try again using your computer instead. Here's how:

1. Make sure that you have the latest version of macOS or the latest version of iTunes.
2. Check that your computer has an Internet connection.
3. With the cable that came with your iPhone, connect your iPhone to your computer. Locate your device on your computer.
4. Wait while your computer detects and activates your iPhone: 

• • If you see an alert that shows "Set up as New" or "Restore from Backup," it means your iPhone is activated.
  • If you get an error message on your computer that says that the SIM card isn't compatible or is invalid, contact your carrier.
  • If you get an error message that says the "activation information was invalid" or "activation information could not be obtained from the device," use recovery mode to restore your iPhone.

If you still can't activate your iPhone, contact Apple Support.

MosesZoltan wrote: "battery was replaced by Apple 76% charging capacity..."

76% is not healthy. So have the weak battery replaced and see if your iPhone can then reach the server:

iPhone Battery & Power Repair

About genuine iPhone batteries

(Articles found by searching Apple's Knowledge Base.)

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MosesZoltan wrote: "...what kind of error is that ?"

Perhaps the kind of error caused by your iPhone 6 Plus's weak battery (76% capacity) not having the strength to connect to the server. Replace the battery.

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MosesZoltan wrote: "...Any other ideas ?"

Does your iPhone 6 Plus still have its original battery?

And what's the Maximum Capacity % here?...

Settings > Battery > Battery Health

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MosesZoltan wrote: "After fully charging it, in the setting, battery capacity shows 100%. "

Moses ~ Battery Capacity isn't dependent on the battery being fully charged. As I'm not convinced you're looking at the right setting, go here:

Settings > Battery > Battery Health

...and then: Take a screenshot on your iPhone and post the screenshot here.

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MosesZoltan wrote: "Replaced the battery, now capacity showing 94%...”

A new replacement battery should be showing 100% max capacity. Was the replacement done by a qualified technician using a genuine iPhone battery?...

About genuine iPhone batteries

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MosesZoltan wrote: "when charged shows 100% capacity..."

But before, you wrote: "now capacity showing 94%"!

Are both those values of 100% & 94% from the Maximum Capacity % here?...

Settings > Battery > Battery Health

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