Installation:
Edit > Preferences > Add-ons > Install > choose the .zip file > Install Add-on > Enable Add-on

Update:
Edit > Preferences > Add-ons > Find 'StashVertexGroup' > Remove > Restart Blender ;) > Reinstall

THE INTERFACE

Where is it ?
The addons interface is in a subpanel of the Vertex Groups panel in the Properties area.

The main buttons:

The STASHED/NO STASH label:

The comment input field and update button:

The stash information area:

The Preferences:

How does it work ?

• The Stash button will copy-and-keep the active vertex group. A text format of vertices/weights of the vertex group is generated internally, making it an 'active stash' with basic information such as the name of the vertex group and its vertex count - the name of the object the vertex group was in, and its total vertex count - the name of the file the object was in - and, a comment that can be added to the stash information by writing into the text input field, pressing Return/Enter and clicking the update comment button .
• The Export button will export the stashed vertex group to a .json file.
• The Import button will import a stashed vertex group from a .json file as the active stash.
• The Append button will import an active stash from a another .blend file (if it has not been exported as a .json file ;)
• The Restore button will write the active stash as a new vertex group or overwrite it if it exists.
• The Refresh button  will update the stash information manually, if the .json file has been changed directly in blenders text editor (which opens up different a different workflow...)
• The Purge button  will delete the active stash.
• The STASHED/NO STASH label underneath the buttons row indicates if there is an active stash or not and is clickable for a popup of the stash information if the Properties area is too narrow to read from.
• The addons functionality is well documented in the popups of buttons and other interface elements, just hover over them to get instant directions :)

GUIDELINES

Restoring Vertex Groups with or without a pose bone deformation:

When Restoring vertex groups with a pose bone deformation (*have the same name as a bone with Deform enabled) it usually requires a normalization of all the other vertex groups with a pose bone deformation of the mesh of that object (*Weights > Normalize All) with the restored vertex group unchanged (*Lock Active enabled), otherwise its affect will unbalance the whole of the deformation of the mesh of the object.

Vertex groups without a pose bone deformation (used for masking, selections, particle systems and such…) or for vertex groups with a pose bone deformation used for another type of operation (like with a VertexWeightMix Modifier for example) usually do not require any normalization operation. It all depends.

To normalize the vertex groups, make sure the restored vertex group is active in the Vertex Groups Panel. In Weight Paint Mode the normalization operator is under Weights > Normalize All > (a pop-up panel ‘Normalize All Vertex Groups’ appears down in the left corner…) > Subset: ‘Deform Pose Bones’ > Lock Active: Enabled

In Edit Mode the normalization operator is under Mesh > Weights > Normalize All...

BENDER VERSIONS

Blender versions that the addon works in:
The addon was tested on Blender 3.0, 3.3, 3.6, 4.0 and 4.1 on mac, linux and windows (since it uses file import/export) and it should work on the in-between versions from 3.0-up (let me know in the 'Report a Bug' of the Preferences area and I will fix the code for that build if possible ;)