Planting shrubs in June?
Yes, you can plant in June, but you should be faithful about giving them a good start, not planting them too deeply and keeping them watered if/when we don't get rain.
Speaking of rain, if your soil is really wet, you need to wait to plant.
A good way to test is to take a handful and squeeze. If it sticks together, it's too wet.
Here is our page on trees and shrubs. Take a look at the Planting Tips publication and the video on planting container plants: