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Things to Do Before Crossing the Land-Border to Johor after Reopening
After nearly two years of travel-restrictions between Singapore and Malaysia, travelling without any requirements for testings and quarantines were finally allowed for border-crossings via land from 1st April 2022.
Instead of an easy land-crossing with just a passport for Singapore passport holders, there are several more things to do:
1. Check Validity of Your Passport
Ensure that your passport has not expired and has at least 6 months of validity.
Due to the COVID-19 pandemic, many Singaporeans with expired passports in the last 2 years had postponed renewing their passports. The re-opening of the border between Singapore and Malaysia for vaccinated travels on 1st April created a rush to apply for new / renewal of passports. Singapore ICA has announced that processing time will take about 1~2 months.

2. Download the MySejahtera App
Note: Effective from 1st August 2022, filling of Traveller's Card in the MySejahtera App is no longer required.
Similar to the TraceTogether app in Singapore, MySejahtera is the equivalent contact tracing application in Malaysia. Travellers to Malaysia will need to download the app and create an account before going over the border.
The following things will need to be done before your first trip:
Step 1: Download the app and create an account — with 4 reCAPTCHA in 4 pages. It will ask you for an address in Malaysia — enter your address in Singapore or just "KSL City" with postcode "80250" and state as "Johor" (you can't select "Singapore").
Step 2: After creating your account, log in to the app and go to "Profile" on the tab bar. Tap the top-right "menu" button and select "My Personal Details". Verify your details.
Note: Nationality will be "Malaysian" by default. Use the Help function and select the option "My Nationality is incorrect..." to correct your Nationality by submitting a photo of your passport.
Step 3: Tap on "MySJ Trace" on the tab bar. You will find the "COVID-19 Vaccination Status" as "Not Vaccinated". Tap on the "Help" button in that box and select "I was vaccinated overseas..." to update your vaccination information (should update at least 2 doses and a booster if any). After submission, it will take about 1-2 days for the status to change to "Fully Vaccinated". Make sure to verify your name and passport number too (see 1. in screenshot below), or your vaccination status will not be updated.

Note: Another alternative will be to use the "Overseas Vaccination Details" option after tapping on "Traveller" on the home page. But it leads to an external webpage instead. It failed on my first attempt to submit the form. However, there are feedbacks that submission using this method will not change the COVID-19 Vaccination Status to "Fully Vaccinated".
Step 4: Before embarking on any trip, tap on the MySejahtera (home) button and select "Traveller", then "Travel for (your name)", answer the 22 mandatory questions... This have to be done for every trip within 7 days before arrival.
Step 5: Once the above are done, tap on "Profile" again, scroll down the page and you should find your Travellers Card and Digital Certificate for COVID-19 Vaccination.
MySejahtera app works pretty well offline — if you do not have mobile data in Malaysia. The Travellers Card and vaccination certificate are not required at Malaysia immigrations. However, it is still advisable to take screenshots of both certificate, just in case you are requested to present them for verification and no network is available.
It is mandatory to use MySejahtera app to scan QR codes at any shops and shopping malls in Malaysia before entry, so do keep the app on your phone. No mobile data is required. (Update 28/4/2022: Effective from 1st May 2022, scanning of QR code with the app at any premises will be optional.)
Read: A Day Trip to Johor Bahru after Border Reopened (and what I experienced)
3. Download SG Arrival Card App
With effect from 15 April 2022, submission of the SG Arrival Card for vaccinated Singapore residents and long-term pass holders will no longer be required at land crossings. Other travellers will still need to submit the arrival cards at the checkpoints.
All travellers (including Singapore citizens) entering Singapore via air and sea will need to submit the SG Arrival Cards within 3 days of arrival in Singapore. You can download the "SG Arrival Card" app from the various app stores for convenience instead of remembering the e-service web link (eservices.ica.gov.sg/sgarrivalcard).