How to convert Clipboard Image BMP to PNG using Pillow package without saving and then loading

I would like to convert an image obtained from the Windows Clipboard to PNG format without having to save and then reload.

As per the code below, I am saving the clipboard image and then reloading it.
Is there a way to convert the image to PNG format without those extra steps, such that the

• PIL.BmpImagePlugin.DibImageFile gets converted to
  

• PIL.PngImagePlugin.PngImageFile

Here is the current code:

from PIL import ImageGrab, Image

# Get the clipboard image
img1 = ImageGrab.grabclipboard()

# Save the image from the clipboard to file
img1.save('paste.png', 'PNG')
print("Image Type1:", type(img1))

# Load the image back in
img2 = Image.open('paste.png')
print("Image Type2:", type(img2))

OUTPUT:

Image Type1: <class 'PIL.BmpImagePlugin.DibImageFile'>
Image Type2: <class 'PIL.PngImagePlugin.PngImageFile'>

As per some help from Seon's comment, this got me on the right track, and fulfilled my requirements.

As per Seon:

"the idea is to save the image to an in-memory BytesIO object, and reload it from there. We're still saving and loading, but not to disk."

Which is exactly what I wanted.
Here is the code I used:

from PIL import ImageGrab, Image
import io


def convertImageFormat(imgObj, outputFormat="PNG"):
    newImgObj = imgObj
    if outputFormat and (imgObj.format != outputFormat):
        imageBytesIO = io.BytesIO()
        imgObj.save(imageBytesIO, outputFormat)
        newImgObj = Image.open(imageBytesIO)
        
    return newImgObj


# Get the clipboard image and convert to PNG
img1 = ImageGrab.grabclipboard()
img2 = convertImageFormat(img1)

# Check the types
print("Image Type1:", type(img1))
print("Image Type2:", type(img2))

OUTPUT:

Image Type1: <class 'PIL.BmpImagePlugin.DibImageFile'>
Image Type2: <class 'PIL.PngImagePlugin.PngImageFile'>