How to build PDF file from binary string returned from a web-service using javascript

Is there any solution like building a pdf file on file system in order
to let the user download it?

Try setting responseType of XMLHttpRequest to blob , substituting download attribute at a element for window.open to allow download of response from XMLHttpRequest as .pdf file

var request = new XMLHttpRequest();
request.open("GET", "/path/to/pdf", true); 
request.responseType = "blob";
request.onload = function (e) {
    if (this.status === 200) {
        // `blob` response
        console.log(this.response);
        // create `objectURL` of `this.response` : `.pdf` as `Blob`
        var file = window.URL.createObjectURL(this.response);
        var a = document.createElement("a");
        a.href = file;
        a.download = this.response.name || "detailPDF";
        document.body.appendChild(a);
        a.click();
        // remove `a` following `Save As` dialog, 
        // `window` regains `focus`
        window.onfocus = function () {                     
          document.body.removeChild(a)
        }
    };
};
request.send();