Example code to use the Translation Manager's internal link updater to update links between two sites.

TranslationManagerNugetUpdater.cs

using System.Linq;
using Umbraco.Core.Models;
using Jumoo.TranslationManager.Core.Services;
using Jumoo.TranslationManager.LinkUpdater;

namespace MyLinkUpdater
{
    /// <summary>
    ///  Update links inside content based on the setup in translation manager.
    /// </summary>
    /// <remarks>
    ///  This should work as long as: 
    ///    1. The sites are in a translation set 
    ///    2. The content nodes are related (this happens when you copy with relate to orginal)
    ///    
    ///  they don't need to have been though the actual translation process, just be linked 
    ///  (and well have sort of the same content!)
    ///  
    ///  you can check links using the LinkedPages setup.
    ///  
    ///  the linkupdater goes through the properties of a node, and finds all links in :
    ///     text, pickers, grid, nested content, etc.. 
    ///     
    ///  When if finds a link that is pointing to something in the 'master' site it uses
    ///  the relation service to find the equivilant in the 'target' site and it updates 
    ///  the link on your target node to point to that. 
    ///  
    ///  if you enumerated through your target site and called this for each node it would update
    ///  all the links
    /// </remarks>
    public class NodeLinkUpdater
    {
        private readonly LinkUpdater _linkUpdater;
        private readonly TranslationSetService _setService;
        private readonly TranslationNodeService _nodeService;

        public NodeLinkUpdater(
            TranslationSetService setService,
            TranslationNodeService nodeService,
            LinkUpdater linkUpdater)
        {
            _nodeService = nodeService;
            _setService = setService;
            _linkUpdater = linkUpdater;
        }

        public void UpdateLinks(IContent node)
        {
            // get you the translation set based on the content node 
            // assume its only in one set?
            
            var set = _setService.GetSetsByTargetPath(node.Path)
                .FirstOrDefault();

            if (set == null) return;
            
            // the 'site' in the set that this node belongs to.
            var targetSite = _setService.GetTargetSite(set, node.Path);
            if (targetSite == null) return;

            // get the content node on the master site, that is the 
            // equivilant of the one we are looking at on the target
            var sourceNode = _nodeService.GetMasterFromTarget(node, set);
            if (sourceNode == null) return;

            // update the links for this page.
            _linkUpdater.ProcessLinks(set, targetSite, sourceNode, node, true, -1);
        }
    }
}