How can I get a user button to create a Python results with its script and properties?

Well, here's one potential solution, as there is no "export button" or "generate user button" option.

First run this script that will store the Python results script and property provider:

pr=ExtAPI.DataModel.GetObjectsByName('Python Result')[0]
 
script=pr.Text 
provider_text=pr.PropertyProviderText
 
f=open(r'wherever\result_script.txt','w') 
f.write(script)
f.write('\n***** delimiter\n') # use whatever delimiter 
f.write(provider_text) 
f.close()

Then use this script to create the user button:

current_object=ExtAPI.DataModel.Tree.FirstActiveObject
 
if current_object.GetType()==Ansys.ACT.Automation.Mechanical.Solution: # user has selected a 'solution' under which the python result will be inserted
    new_presult=current_object.AddPythonResult()
    f=open(r'wherever\result_script.txt','r') # script content stored somewhere
    script=''
    provider_text=''
    line=f.readline()
    # read script text
    while line.find('***** delimiter')==-1: # same delimiter as above 
        script+=line
        line=f.readline()
    line=f.readline()
    # read provider text
    while line:
        provider_text+=line
        line=f.readline()
        
    
    f.close()
    new_presult.PropertyProviderText=provider_text
    new_presult.Text=script
    new_presult.Connect()
    new_presult.ReloadProperties()