The guidance states that your new FLR(M) visa will be made valid from the expiry date of your previous visa, so you should get the extra time.
However, I don’t think anyone has mentioned recently whether this has actually been the case or not.
If you apply on May 22nd, however, it should not expire before you qualify for ILR because UKVI shouldn’t let that happen. At the earliest, the FLR(M) should start on June 19th. At the latest it should start in September.
Either way, I wouldn’t worry about it. If you want to apply in May, then go ahead and apply. If you want to wait until September, then wait.
The only thing to consider is that the IHS surcharge will double from £500 to £1,000 at some point this year, but we don’t know when that will be, so I would apply earlier rather than later, to potentially save yourself £500.
Is there a particular reason why you want to apply in person? FLR(M) applications are only taking about 5-8 weeks by post (and they haven’t taken longer than 8 weeks for a few years now), so unless you need to travel urgently, I would probably save the £600 for in person and apply by post. That will also guarantee extra time on your visa because it won’t start until it has been issued at the earliest. So even if you apply in May, if it’s not issued until July, your FLR(M) will be valid until at least Jan 2021.
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