user23596: In a situation where a mobile phone rings in the middle of the game should the offender's opponent call the arbiter and claim the win.
If claiming is not needed and if the arbiter decides to mark the game as a loss for the offender is it possible to continue the game based on mutual agreement between the players or is the arbiter decision final?

user32155: According to Article 12.3 b of FIDE Handbook of Laws Of Chess:

Without the permission of the arbiter a player is forbidden to have a
mobile phone or other electronic means of communication in the playing
venue, unless they are completely switched off. If any such device
produces a sound, the player shall lose the game.

I think this will answer your question.


is it possible to continue the game based on mutual agreement between
the players?

Rules are rules. They are the same for everyone so there's no possibility of mutual agreement between players. Otherwise, this would lead to inequalities.


In a situation where a mobile phone rings in the middle of the game should the offender's opponent call the arbiter and claim the win.

Well, that's the only option left out there. He/She cannot claim the win on their own. They need to call out the Arbiter and let him/her handle the situation.

Example/Similar case:
The latest similar case which I could find on the internet was Nigel Short vs Lorenzo Candian. In their match, Lorenzo was winning his game against Nigel but he lost when his phone rang. Here's a video which you can take a look at to know more about it.

user4418: There are two main sections in the FIDE Laws of Chess: BASIC RULES OF PLAY, which describes the basic rules of the game which pretty much apply regardless of whether the game is played as part of a formal competition or not, and COMPETITION RULES, which describes additional formal rules for FIDE controller competitions.
The word "arbiter" appears only once in the BASIC RULES OF PLAY and I almost think that's a mistake. Arbiters only have a role to play in formal competitions. There are more than 60 occurrences of "arbiter" in the seven articles which comprise the COMPETITION RULES.
Long story short: the arbiter decides what happens in the formal competition. You can decide what happens outside the competition.
So:

is it possible to continue the game based on mutual agreement between the players or is the arbiter decision final?

As regards the competition, the arbiter's word is final and the result gets recorded as a loss for the player whose phone rang. As regards completing the game, most tournaments will have an analysis area. You and your opponent are perfectly free to go there, set your game up and continue.
This is a principle which predates FIDE by at least 1900 years.

23596: <p>In a situation where a mobile phone rings in the middle of the game should the offender's opponent call the arbiter and claim the win.<br />
If claiming is not needed and if the arbiter decides to mark the game as a loss for the offender is it possible to continue the game based on mutual agreement between the players or is the arbiter decision final?</p>
 32155: <p>According to <strong>Article 12.3 b</strong> of <a href="https://www.fide.com/FIDE/handbook/LawsOfChess.pdf" rel="nofollow noreferrer">FIDE Handbook of Laws Of Chess</a>:</p>
<blockquote>
<p>Without the permission of the arbiter a player is forbidden to have a
mobile phone or other electronic means of communication in the playing
venue, unless they are completely switched off. If any such device
produces a sound, the player shall lose the game.</p>
</blockquote>
<p>I think this will answer your question.</p>
<hr />
<blockquote>
<p>is it possible to continue the game based on mutual agreement between
the players?</p>
</blockquote>
<p>Rules are rules. They are the same for everyone so there's no possibility of mutual agreement between players. Otherwise, this would lead to inequalities.</p>
<hr />
<blockquote>
<p>In a situation where a mobile phone rings in the middle of the game should the offender's opponent call the arbiter and claim the win.</p>
</blockquote>
<p>Well, that's the only option left out there. He/She cannot claim the win on their own. They need to call out the Arbiter and let him/her handle the situation.</p>
<hr />
<p><strong>Example/Similar case:</strong></p>
<p>The latest similar case which I could find on the internet was Nigel Short vs Lorenzo Candian. In their match, Lorenzo was winning his game against Nigel but he lost when his phone rang. Here's a <a href="https://www.youtube.com/watch?v=m3CyBR2mIuU" rel="nofollow noreferrer">video</a> which you can take a look at to know more about it.</p>
 4418: <p>There are two main sections in the <a href="https://handbook.fide.com/chapter/E012018" rel="nofollow noreferrer">FIDE Laws of Chess</a>: <strong>BASIC RULES OF PLAY</strong>, which describes the basic rules of the game which pretty much apply regardless of whether the game is played as part of a formal competition or not, and <strong>COMPETITION RULES</strong>, which describes additional formal rules for FIDE controller competitions.</p>
<p>The word &quot;arbiter&quot; appears only once in the BASIC RULES OF PLAY and I almost think that's a mistake. Arbiters only have a role to play in formal competitions. There are more than 60 occurrences of &quot;arbiter&quot; in the seven articles which comprise the COMPETITION RULES.</p>
<p>Long story short: the arbiter decides what happens in the formal competition. You can decide what happens outside the competition.</p>
<p>So:</p>
<blockquote>
<p>is it possible to continue the game based on mutual agreement between the players or is the arbiter decision final?</p>
</blockquote>
<p>As regards the competition, the arbiter's word is final and the result gets recorded as a loss for the player whose phone rang. As regards completing the game, most tournaments will have an analysis area. You and your opponent are perfectly free to go there, set your game up and continue.</p>
<p>This is <a href="https://biblehub.com/mark/12-17.htm" rel="nofollow noreferrer">a principle</a> which predates FIDE by at least 1900 years.</p>
