//js/get_var.js
setTimeout(function() {
    var info = false;
    if (window.mySummaryPrefix) {
        info = {mySummaryPrefix:mySummaryPrefix}
    }
    document.dispatchEvent(new CustomEvent('my_event_connectExtension', {
        detail: info
    }));
}, 0);

...
  "web_accessible_resources": ["js/get_var.js"]
...

//content_script.js
function askForValue(){
    var scriptTag = document.createElement('script');
    scriptTag.src = chrome.extension.getURL('js/get_var.js');
    (document.head||document.documentElement).appendChild(scriptTag);
    scriptTag.onload = function() {
        scriptTag.parentNode.removeChild(scriptTag);
    };
}

document.addEventListener('my_event_connectExtension', function(e) {
    if (e.detail) {
        var info = e.detail && {'info': e.detail} || false;
        console.log(info);
    }
});

document.addEventListener('DOMContentLoaded', function() {
     askForValue();
}

"content_scripts": [{
    "matches": ["https://*/*"], /* your url matchs */
    "js": ["js/content_script.js"]
  }],

//from popup.js
...
chrome.tabs.getSelected(null, function(tab) {
    chrome.tabs.sendMessage(tab.id, {
        'action': 'myExtension:myAction'
    }, function(result){
        var info = result && result.info;
    });
});
...

chrome.runtime.onMessage.addListener(function(request, sender, callback){
    if (request.action === 'myExtension:myAction') { ...