Often plants rooted in water have a weaker root structure. I would suggest that you get some perlite. Put the rooted stems in a pot with drainage holes, pour in the perlite to cover just above where the roots meet the plant stem, water well and keep slightly moist for about one month. This will give the roots an opportunity to develop a stronger root structure. Then you can try potting up again.

If you try inserting the stems with roots into the perlite instead of pouring the perlite over the roots, you risk tearing and damaging the roots as the perlite is abrasive.

Newt

Newt

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When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.