I want to say about someone that he is "not forgetful" or probably "easy to remember things, hard to forget". But I feel like it's too mouthful, and English probably has the term for this, but I don't know how to search for things like this. Can you help me what is the term for "not forgetful"? Thanks.
The most common ways to say that someone is good at remembering things include:
He has a good memory.
She has an excellent memory.
Adjectives such as "mindful" are rarely good substitutes.
"Mindful" means keeping something in mind, and is almost always followed by a description of the thing:
He is mindful of his obligations. (= He is aware of his obliations.)
"Attentive" means either that someone listens well (for example, in class) or that they pay attention to particular things:
She is attentive to the nuances of what people say.
"Retentive" most often describes memory rather than a person ("she has a retentive memory"), but ODO also gives this example:
She's very retentive of any facts about the culture, especially about the language.
Some common antonyms to forgetful include mindful, retentive, and attentive.
But I find the most colorful way to describe someone who never forgets is to call them an elephant. Why an elephant? Because an old expression goes:
An elephant never forgets.
Though if you decide to call someone an elephant, be prepared to explain this, as without context, someone might think you were calling them fat. ;)
One way you could say this is that someone has a photographic memory.
However, before you introduce this into your vocabulary, you should know: you'd be using this in a figurative and not literal sense.
Wikipedia says that photographic memory refers to "the ability to recall pages of text or numbers, or similar, in great detail" and also mentions that "true photographic memory has never been demonstrated to exist."
So, I might say, "Linda has a photographic memory," but I'd most likely not be referring to the clinical phenomenon; rather, I'd mean that Linda is not forgetful but good at remembering things.
One way writers might distinguish between the two is to use near or almost. Collins has an example usage from the Sunday Times which reads:
I was to discover that he had an almost photographic memory.
I've seen other instances where the more figurative use of this term is employed with a dash of hyperbole, such as when Bruce Benderson wrote in his autobiographical work:
If I brought up this episode, she could recall every syllable of it. My mother has a photographic memory.
As a matter of fact, the adjective "memorious" sounds pleasant for a person having a good memory, but, unfortunately, it is too obsolete to be used in modern English.
The phrases that are very common and idiomatic are "a good memory" and "a photographic memory". The former is more common than the latter.
He has a good memory.
He has a photographic memory.
You can also say "He has an amazing memory".