My two answers for two approaches to the problem (both developed thanks to ccprog):
1. Setting char by class definition:
In that approach we can define element that way:
<text class="fa fa-globe"></text>
And next run that code:
var icons = document.querySelectorAll("text.fa");
  // I want to modify only icons in SVG text elements
var stylesheets = Array.from(document.styleSheets);
  // In my project FontAwesome styles are compiled with other file,
  // so I search for rules in all CSS files
// Getting rules from stylesheets is slightly more complicated:
var rules = stylesheets.map(function(ss) {
  return ss && ss.cssRules ? Array.from(ss.cssRules) : [];
})
rules = [].concat.apply([], rules);
// Rest the same:
icons.forEach(function (icon) {
  var name = Array.from(icon.classList).find(function (c) {
      return c.startsWith('fa-');
  });
  var style = rules.find(function (r) {
      return r.selectorText && r.selectorText.endsWith(name + "::before");
  }).style;
  icon.textContent = style.content.substr(1,1);
});
But I had some problems with that approach, so I developed the second one.
2. Getting char with function:
const getFontAwesomeIconChar = (name) => {
  var stylesheets = Array.from(document.styleSheets);
  var rules = stylesheets.map(function(ss) {
    return ss && ss.cssRules ? Array.from(ss.cssRules) : [];
  })
  rules = [].concat.apply([], rules);
  var style = rules.find(function (r) {
    return r.selectorText && r.selectorText.endsWith(name + "::before");
  }).style;
  return style.content.substr(1,1);
}
Having that funcion defined we can do something like this (example with React syntax):
<text>{getFontAwesomeIconChar('fa-globe')}</text>