You can use dead keys and character combinations to get characters the keyboard doesn't support directly. This is what's done in France, where the standard AZERTY keyboard doesn't have keys for every French letter. For some letters it also only has a lowercase version, not uppercase. (Accents are optional on uppercase letters in French because... who knows why.) There is a dedicated key for the letter ù though, which only appears in a single word of the French language.
Unlike what some french believe, they are not supposed to be optional:
http://www.academie-francaise.fr/questions-de-langue#5_stron...
In spanish it used to be the same. Old printing technologies were not so flexible as a screen, so for large imprints it made more sense to have all letters be the same size whilst not wasting space above the letters.
Couldn't your friend use trigraphs (https://en.wikipedia.org/wiki/Digraphs_and_trigraphs) in place of these characters?
[1] https://www.microsoft.com/en-us/download/details.aspx?id=223...
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[1] Most keyboards had the Estonian layout in early 2000s, but they soon rapidly lost market share, mostly due to laptops if I had to guess why.
[2] Why not use US ANSI layout in the OS to match the keyboard? Because it doesn't contain characters required to type Estonian words.