Sharepoint - No way to stop sending a welcome email when granting permissions in SharePoint 2013

When you add a user / group in SharePoint, you should see "Send an email invitation" check box to control whether or not send the welcome e-mail to the new users. You could clear that check box and it should fix your problem.

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Also, there are some situations when "Send an email invitation" is hidden. I checked dialog's code-behind by reflector and find that:

Part of InitPage method of AclInv.cs:

if (isEmailServerSet)
  {
    if (object.get_IsCompatibilityLevel15Up())
    {
      this.PanelSendEmail.Visible = true;
      this.PanelEmailBody.Visible = true;
      this.txtEmailSubject.Text = SPResource.GetString(CultureInfo.CurrentCulture, "ACLInviteDefaultSubject", (object) this.Web.CurrentUser.Name, (object) this.TargetObjectTitle);
      if (this.CanSendLink)
      {
        this.PanelRequireSignIn.Visible = true;
        this.InitRequireSignInLabel();
      }
      this.peoplePicker.set_VisibleSuggestions(5);
    }
    else
      this.ifsSendEmail.Visible = true;
  }

As you can see sharepoint checks "isEmailServerSet" before setting visibility to inviation configuration panels.

As the result, you need to configure outgoing e-mail settings in CA (Central Administration -> System settings -> Configure outgoing e-mail settings) to make invitation configuration visible in "Share" dialog.