If both people are on the same tree then you can connect them by clicking on the sign o the person's name card. If they aren't in the same tree, I don't think there is anything you can do. I could be wrong on the last part, but I don't think so.
What you can do is work with shadow records. On your tree, you create a new person by the name "continuation cf. such-and-such website." Then you add a fact to that record that contains the link to that webpage. The manager of the other tree can do the same, pointing to your website.
This is evidently not the same as merging the two trees, because you cannot search across tree borders, but it is better than nothing.
The primary stumbling block with merging trees are the record numbers. Each tree has record numbers starting with #1. By merging the trees, you would need to renumber all of the records. Otherwise the software will get confused.
There are certainly tools available outside MyHeritage / Family Tree Builder that will allow you to merge two separate GED files, but using any of those opens another can of worms, because you will at least lose all of your photographs, since MyHeritage / Family Tree Builder will not reimport them together with the merged tree.