How to put the modal verb "may" into the correct tense?

Question

I don't understand how transform the following sentences using the following tenses. So that it has the same meaning as the first one.

How to put the modal verb "may" into the correct tense?

Present simple: She may invite friends. Past simple: She _____ invite friends. Present perfect simple: She _____ invite friends. Will-Future: She _____ invite friends.

https://www.english-4u.de/en/grammar-exercises/modal-verbs2.htm

Present simple: They must work harder. Past simple: They had to work harder. Present perfect simple: They have had to work harder. Will-Future: They will have to work harder.

Present simple: We can help you in the garden. Past simple: We could help you in the garden. Present perfect simple: We have been able to help you in the garden. Will-Future: We will be able to help you in the garden.

Answer 1

May, like might, can, could, will, would, shall, should, must, and sometimes need and dare, is a Modal Auxiliary Verb. Modal auxiliary verbs are always the first auxiliary verb in a verb phrase, and they are not inflected for tense.

Therefore, modal auxiliary verbs do not occur in any tense, either present or past. Alternatively, if you don't like that statement, you can say they're always present tense (though that's just an arbitrary choice; they aren't marked in any way). And they certainly don't represent time.

English modals used to be inflected (and their German cognates still are), but now they're all considered just Modals, outside verbal morphology. The fact that some of them came from a preterite root and some of them don't is really irrelevant because it's almost never used to represent tense.

So if that's a question from a textbook or an English teacher, find a better one; whoever asked that question doesn't understand what it means

Answer 2

May is a highly irregular verb, and unlike other verbal auxilliaries such as be, have etc it does not have a conjugated past tense, nor participles.

And as @Shoe demonstrates the answer divides between the deontic and the epistemic. (see comment above)

The way I would deal with the three instances, under each of those headings, would be as follows. I can confirm that they are all perfectly idiomatic and say what I think you may want to say.

In some instances the adverb maybe does the work.

Epistemic

Past simple: Maybe she invited friends.

Present perfect simple: She may have invited friends.

Future Maybe she will invite friends

Deontic

Past simple: She was permitted/allowed to invite friends.

Present perfect: She has been permitted/allowed to invite friends

Future: She will be permitted/allowed to invite friends

Perhaps this is an answer more suitable for English Language Learners. I have no doubt that one of our accomplished linguisticians (which I am not) can supply a more theoretical explanation.