Answer: You may be able to transplant the shrubs if they are of a manageable size and you can dig them up with most of their roots intact. Mature shrubs are much more difficult to move. Some types of shrubs are easier to transplant, with deep rooted plants being more difficult. You would replant immediately at the same depth as they grew before and then care for them as you would any newly planted shrub, watering as needed to keep the soil damp for the rest of the growing season. Without knowing what kind of shrub, it is difficult to be more specific.
Cats can sometimes be deterred by using the spray-on repellents labeled for cats. Or, sometimes changing to a different mulch material will be less attractive to them. There are also motion activated water sprays and sonic repellers available. Spreading wire mesh or thorny branches on the soil surface of your garden areas may discourage them as well. You might also contact your local animal control authority if they are strays. Finally, quite often this is a seasonal problem and they disperse as the summer comes. I hope this helps.
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